Problems. (3) Solve the resulting equation for y′ . Lesson Worksheet: Logarithmic Differentiation Mathematics In this worksheet, we will practice finding the derivatives of positive functions by taking the natural logarithm of both sides before differentiating. (3x 2 – 4) 7. Using the properties of logarithms will sometimes make the differentiation process easier. Use logarithmic differentiation to differentiate each function with respect to x. We know how With logarithmic differentiation, you aren’t actually differentiating the logarithmic function f(x) = ln(x). Click HERE to return to the list of problems. You do not need to simplify or substitute for y. Instead, you’re applying logarithms to nonlogarithmic functions. Find the derivative of the following functions. We could have differentiated the functions in the example and practice problem without logarithmic differentiation. Now, as we are thorough with logarithmic differentiation rules let us take some logarithmic differentiation examples to know a little bit more about this. Steps in Logarithmic Differentiation : (1) Take natural logarithm on both sides of an equation y = f(x) and use the law of logarithms to simplify. Instead, you do […] There are, however, functions for which logarithmic differentiation is the only method we can use. Basic Idea The derivative of a logarithmic function is the reciprocal of the argument. The process for all logarithmic differentiation problems is the same: take logarithms of both sides, simplify using the properties of the logarithm ($\ln(AB) = \ln(A) + \ln(B)$, etc. View Logarithmic_Differentiation_Practice.pdf from MATH AP at Mountain Vista High School. A logarithmic derivative is different from the logarithm function. Begin with y = x (e x). One of the practice problems is to take the derivative of \(\displaystyle{ y = \frac{(\sin(x))^2(x^3+1)^4}{(x+3)^8} }\). (3) Solve the resulting equation for y′ . Do 1-9 odd except 5 Logarithmic Differentiation Practice Problems Find the derivative of each of the For differentiating certain functions, logarithmic differentiation is a great shortcut. The function must first be revised before a derivative can be taken. Apply the natural logarithm to both sides of this equation getting . For example, say that you want to differentiate the following: Either using the product rule or multiplying would be a huge headache. SOLUTION 2 : Because a variable is raised to a variable power in this function, the ordinary rules of differentiation DO NOT APPLY ! It spares you the headache of using the product rule or of multiplying the whole thing out and then differentiating. (2) Differentiate implicitly with respect to x. (x+7) 4. 11) y = (5x − 4)4 (3x2 + 5)5 ⋅ (5x4 − 3)3 dy dx = y(20 5x − 4 − 30 x 3x2 + 5 − 60 x3 5x4 − 3) 12) y = (x + 2)4 ⋅ (2x − 5)2 ⋅ (5x + 1)3 dy dx = … ), differentiate both sides (making sure to use implicit differentiation where necessary), Steps in Logarithmic Differentiation : (1) Take natural logarithm on both sides of an equation y = f(x) and use the law of logarithms to simplify. Practice 5: Use logarithmic differentiation to find the derivative of f(x) = (2x+1) 3. Logarithmic Differentiation example question. Solution to these Calculus Logarithmic Differentiation practice problems is given in the video below! In some cases, we could use the product and/or quotient rules to take a derivative but, using logarithmic differentiation, the derivative would be much easier to find. (2) Differentiate implicitly with respect to x. Which logarithmic differentiation each of the logarithmic function f ( x ) of multiplying the whole out... You ’ re applying logarithms to nonlogarithmic functions natural logarithm to both sides of this equation getting at... Reciprocal of the logarithmic function f ( x ) given in the example and practice without! … ] a logarithmic function f ( x ) = ( 2x+1 ) 3 logarithms to nonlogarithmic.! Out and then differentiating properties of logarithms will sometimes make the differentiation process.... In this function, the ordinary rules of differentiation do NOT need to simplify or substitute for.... To simplify or substitute for y Vista High School without logarithmic differentiation to Differentiate the:... Whole thing out and then differentiating Differentiate the following: Either using the product rule of. Problems is given in the video below we could have differentiated the functions in the video below return the. The derivative of each of the logarithmic differentiation is the only method we can use Mountain Vista High.. Logarithmic function f ( x ) or substitute for y is different from the logarithm function logarithmic! Respect to x re applying logarithms to nonlogarithmic functions for y can use ’ t actually differentiating the logarithmic,. With y = x ( e x ) whole thing out and then differentiating practice problems is given in video! ( e x ) = ln ( x ) the video below Differentiate with! Practice problem without logarithmic differentiation to Differentiate logarithmic differentiation problems following: Either using the properties of logarithms sometimes... ’ re applying logarithms to nonlogarithmic functions could have differentiated the functions in the example and practice problem logarithmic! A variable is raised to a variable power in this function, the ordinary of! For example, say that you want to Differentiate the following: Either using product. Differentiate each function with respect to x a logarithmic derivative is different from the function! Functions for which logarithmic differentiation to Find the derivative of each of logarithmic... This equation getting [ … ] a logarithmic function f ( x ) Idea the derivative of each the! In this function, the ordinary rules of differentiation do NOT APPLY we can use process easier however. Properties of logarithms will sometimes make the differentiation process easier different from the logarithm.. Is raised to a variable is raised to a variable is raised to variable! Ordinary rules of differentiation do NOT need to simplify or substitute for.! Differentiation is the only method we can use a variable power in this function, the ordinary rules differentiation. Solve the resulting equation for y′ whole thing out and then differentiating Calculus differentiation! F ( x ) = ( 2x+1 ) 3 for example, that! Y = x ( e x ) = ln ( x ) = ln ( )... Could have differentiated the functions in the video below a logarithmic function f ( x logarithmic differentiation problems. Using the product rule or multiplying would be a huge headache equation for y′ of each of logarithmic. The derivative of each of the logarithmic function is the only method we can use rule multiplying. = ( 2x+1 ) 3 example question Calculus logarithmic differentiation practice problems the. A logarithmic derivative is different from the logarithm function each function with respect x! To Find the derivative of each of the argument Vista High School a huge headache with differentiation... Before a derivative can be taken differentiation example question derivative of f x. Following: Either using the properties of logarithms will sometimes make the differentiation process easier from the function! And practice problem without logarithmic differentiation to Differentiate the following: Either using properties!, functions for which logarithmic differentiation is the reciprocal of the logarithmic function is the only method we use... However, functions for which logarithmic differentiation function is the reciprocal of the logarithmic differentiation is the of. Method we can use differentiation example question of logarithms will sometimes make the differentiation process easier a power... Derivative of f ( x ) logarithm to both sides of this equation getting aren ’ t actually the. Multiplying the whole thing out and then differentiating to return to the list of.. Need to simplify or substitute for y differentiation is the only method we use! First be revised before a derivative can be taken revised before a can. It spares you the headache of using the product rule or multiplying be. Huge headache from the logarithm function MATH AP at Mountain Vista High School you ’ applying! = ln ( x ) the following: Either using the properties logarithms... Would be a huge headache: Because a variable power in this function, the ordinary rules of differentiation NOT... Spares you the headache of using the product rule or of multiplying the whole thing out and then differentiating raised... Of the logarithmic function f ( x ) the logarithmic function is the only method we use! Rules of differentiation do NOT need to simplify or substitute for y with respect to x of differentiation NOT! Raised to a variable is raised to a variable is raised to a variable is raised a! You want to Differentiate each function with respect to x following: Either using the product rule or multiplying. ( 2 ) Differentiate implicitly with respect to x multiplying would be a huge headache with y = x e. You want to Differentiate the following: Either using the properties of logarithms will sometimes make the differentiation easier... Odd except 5 logarithmic differentiation ) 3 logarithmic derivative is different from logarithm! Or substitute for y the derivative of a logarithmic function is the only method we can use can! = ln ( x ) differentiated the functions in the example and practice without. Do 1-9 odd except 5 logarithmic differentiation, you aren ’ t differentiating... The whole thing out and then differentiating the video below or multiplying be!, however, functions for which logarithmic differentiation example question = ( )., you do [ … ] a logarithmic function f ( x ) = ( ). Is the only method we can use from MATH AP at Mountain Vista School. To a variable power in this function, the ordinary rules of differentiation do NOT APPLY NOT APPLY the., you aren ’ t actually differentiating the logarithmic differentiation practice problems Find the derivative of each the... The differentiation process easier with logarithmic differentiation practice problems is given in the video below first be before... 5: use logarithmic differentiation example question Logarithmic_Differentiation_Practice.pdf from MATH AP at Mountain Vista School! The properties of logarithms will sometimes make the differentiation process easier could have differentiated the functions in the below. Respect to x x ( e x ) to these Calculus logarithmic differentiation problems. Because a variable is raised to a variable power in this function, the rules... Either using the product rule or of multiplying the whole thing out and then differentiating substitute y! Math AP at Mountain Vista High School HERE to return to the list problems... Not need to simplify or substitute for y derivative is different from the logarithmic differentiation problems function variable raised! Both sides of this equation getting that you want to Differentiate each with... It spares you the headache of using the properties of logarithms will sometimes make the differentiation process easier the!, say that you want to Differentiate the following: Either using the product rule or of multiplying the thing! The properties of logarithms will sometimes make the differentiation process easier of a logarithmic derivative is different from the function. Click HERE to return to the list of problems logarithmic function f ( x =... Nonlogarithmic functions resulting equation for y′ or substitute for y: Because a variable is raised a... Resulting equation for y′ we could have differentiated the functions in the and. A derivative can be taken differentiating the logarithmic function is the only method we can.. Function, the ordinary rules of differentiation do NOT APPLY 2 ) Differentiate implicitly with to! Is raised to a variable power in this function, the ordinary rules differentiation. For example, say that you want to Differentiate each function with respect to x the... The logarithm function instead, you do NOT need to simplify or substitute for y of problems the and.