Implicit Differentiation

Logarithmic differentiation on quotients, powers, and roots — take logs of both sides to turn products into sums, then differentiate implicitly and solve.

Calculus Lab Manual, Implicit Differentiation

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3 exercises

Exercise 4

Use the process of logarithmic differentiation to find a first derivative formula for each of the following functions.

$y=\dfrac{x\fe{\sin}{x}}{\sqrt{x-1}}$

2.5

Exercise 5

Use the process of logarithmic differentiation to find a first derivative formula for each of the following functions.

$y=\dfrac{e^{2x}}{\fe{\sin^4}{x}\sqrt[4]{x^5}}$

2.5

Exercise 6

Use the process of logarithmic differentiation to find a first derivative formula for each of the following functions.

$y=\dfrac{\fe{\ln}{4x^3}}{x^5\fe{\ln}{x}}$

2.5