Problem

Find $ y' $ if $ y $ = In $ (x^2 + y^2). $

03:07

Problem 50 Medium Difficulty

Use logarithmic differentiation to find the derivative of the function.

$ y = (\ln x)^{\cos x} $

Name: use logarithmic differentiation to find the derivative of the function y ln xcos x
Uploaded: 2019-12-05
Duration: 1 min 24 s
Channel: Numerade
Description: Use logarithmic differentiation to find the derivative of the function. $ y = (\ln x)^{\cos x} $

Answer

$\frac{d y}{d x}=(\ln x)^{\cos x}\left[\frac{\cos x}{x \ln x}-\sin x \cdot \ln (\ln x)\right]$

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Video Transcript

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Topics

Derivatives

Differentiation

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 6

Derivatives of Logarithmic Functions