Which of the following is d y / d x if y=cos^2(x^3+x^2) ? (A) -2(3 x^2+2 x) (B) -(3 x^2+2 x) cos

Name: Problem 73, Chapter 4: Calculus: Graphical, Numerical, Algebraic
Uploaded: 2021-08-28T08:13:42-08:00
Duration: 1 min 39 s
Channel: Adrian Co
Description: Which of the following is d y / d x if y=cos^2(x^3+x^2) ? (A) -2(3 x^2+2 x) (B) -(3 x^2+2 x) cos(x^3+x^2) sin(x^3+x^2) (C) -2(3 x^2+2 x) cos(x^3+x^2) sin(x^3+x^2) (D) 2(3 x^2+2 x) cos(x^3+x^2) sin(x^3+x^2) (E) 2(3 x^2+2 x)

step 1 the derivative of this and then figure out which one of the choices this the answer would be. Le

Question

Which of the following is $d y / d x$ if $y=\cos ^{2}\left(x^{3}+x^{2}\right) ?$ (A) $-2\left(3 x^{2}+2 x\right)$ (B) $-\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)$ (C) $-2\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)$ (D) $2\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)$ (E) $2\left(3 x^{2}+2 x\right)$

   Which of the following is $d y / d x$ if $y=\cos ^{2}\left(x^{3}+x^{2}\right) ?$
(A) $-2\left(3 x^{2}+2 x\right)$
(B) $-\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)$
(C) $-2\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)$
(D) $2\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)$
(E) $2\left(3 x^{2}+2 x\right)$

Calculus: Graphical, Numerical, Algebraic

Ross L. Finney,… 5th Edition

Chapter 4, Problem 73

Instant Answer

Solved by Expert Adrian Co

08/28/2021

Step 1

We need to find the derivative of this function. We will use the chain rule to find the derivative. The chain rule states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function. Show more…

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Which of the following is $d y / d x$ if $y=\cos ^{2}\left(x^{3}+x^{2}\right) ?$ (A) $-2\left(3 x^{2}+2 x\right)$ (B) $-\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)$ (C) $-2\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)$ (D) $2\left(3 x^{2}+2 x\right) \cos \left(x^{3}+x^{2}\right) \sin \left(x^{3}+x^{2}\right)$ (E) $2\left(3 x^{2}+2 x\right)$

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Key Concepts

Chain Rule

The chain rule is a fundamental concept in calculus used to differentiate composite functions. It involves taking the derivative of the outer function evaluated at the inner function and multiplying it by the derivative of the inner function.

Trigonometric Differentiation

This concept involves finding the derivatives of trigonometric functions, such as recognizing that the derivative of cosine is negative sine. This is essential when differentiating expressions that include trigonometric functions.

Power Rule for Composite Functions

This rule is used to differentiate functions raised to a power. When a function is expressed as another function raised to an exponent, the derivative is found by multiplying the exponent with the function raised to one less power and then applying the chain rule on the inner function.

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