Problem

Regard $ y $ as the independent variable and $ x …

01:52

Problem 22 Easy Difficulty

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

Answer

$\frac{d x}{d y}=\frac{-2 x^{4} y+x^{3}-6 x y^{2}}{4 x^{3} y^{2}-3 x^{2} y+2 y^{3}}$

More Answers

01:25

Frank L.

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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Video Transcript

if this problem were given any question on and years to find their function. G when exes. Zira, let's first find the value of that function when x zero Solis for G zero. So we're gonna play zero in terms of eggs. So we have g 00 was zero times sine GOP zero as people to zero this term is zero. So from this BC, that G o P zero is zero. And let's tag narrative All think of the question. You have G primal X plus breaking news for a cool for a second term of left hand side, we have a sign your ex waas um X times consign g o eggs times deeper X is equal to x. No less plays you're in. You have g p zero plus sign G off zero plus zero times. Co sign g +00 times zero is zero. This storm is zero. We have signed you up zero but be known at jobs series itself, his ears off signing zero sign of serious. You're so from this we see that GI problems here put there a physical zero. So Jeep ERM of zero is the U

Doruk I.

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

Heather Z.

Oregon State University

Kayleah T.

Harvey Mudd College

Michael J.

Idaho State University