# logarithmic differentiation problems

View Logarithmic_Differentiation_Practice.pdf from MATH AP at Mountain Vista High School. Apply the natural logarithm to both sides of this equation getting . SOLUTION 2 : Because a variable is raised to a variable power in this function, the ordinary rules of differentiation DO NOT APPLY ! 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. 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. (2) Differentiate implicitly with respect to x. Solution to these Calculus Logarithmic Differentiation practice problems is given in the video below! We could have differentiated the functions in the example and practice problem without logarithmic differentiation. With logarithmic differentiation, you aren’t actually differentiating the logarithmic function f(x) = ln(x). Basic Idea The derivative of a logarithmic function is the reciprocal of the argument. ), differentiate both sides (making sure to use implicit differentiation where necessary), (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 = … We know how You do not need to simplify or substitute for y. Logarithmic Differentiation example question. Instead, you’re applying logarithms to nonlogarithmic functions. The function must first be revised before a derivative can be taken. For differentiating certain functions, logarithmic differentiation is a great shortcut. Practice 5: Use logarithmic differentiation to find the derivative of f(x) = (2x+1) 3. It spares you the headache of using the product rule or of multiplying the whole thing out and then differentiating. Problems. Do 1-9 odd except 5 Logarithmic Differentiation Practice Problems Find the derivative of each of the Using the properties of logarithms will sometimes make the differentiation process easier. 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. (3x 2 – 4) 7. (3) Solve the resulting equation for y′ . Use logarithmic differentiation to differentiate each function with respect to x. 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. Find the derivative of the following functions. A logarithmic derivative is different from the logarithm function. (2) Differentiate implicitly with respect to x. Click HERE to return to the list of problems. 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