Problem

If $ g(x) + x \sin g(x) = x^2, $ find $ g'(0). $

01:34

Problem 21 Easy Difficulty

If $ f(x) + x^2[f(x)]^3 = 10 $ and $ f(1) = 2, $ find $ f'(1). $

Answer

$f^{\prime}(1)=\frac{-16}{13}$

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Discussion

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Watch More Solved Questions in Chapter 3

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Video Transcript

So if you have this and give you eff off one Finance prime one. So here we take the derivative on both sides. The second term we use the product rule and Cheryl Sorry, this should be. Plus, it was a product. Russo thiss plus the first part times at the review of the second Power is chair or three f o x square of pry affects Ryan. Sighs of constants are details that the ring with him she gives you zero and you clubbing one. So you have private fun plus two times f Cuba's foreign killed eight plus three extra problem one. So disappear. My mommy is one. So you have the right and how and the FX is so if one is to so if one squares for half price for the hose hero. So you have one plus twelve this certain so certainly have pry off one horse. Negative sixteen. So that should keeps us f proffer one ecos negative sixteen over thirty

Frank L.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 5

Implicit Differentiation

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Catherine R.

Missouri State University

Samuel H.

University of Nottingham

Joseph L.

Boston College