Question

Find $d y / d x$. $$y=(1+\cos 2 x)^{2}$$

Name: Problem 22, Chapter 4: Calculus: Graphical, Numerical, Algebraic
Uploaded: 2021-08-28T07:37:32-08:00
Duration: 1 min 20 s
Channel: Adrian Co
Description: Find d y / d x. y=(1+cos2 x)^2

   Find $d y / d x$.

$$y=(1+\cos 2 x)^{2}$$

Calculus: Graphical, Numerical, Algebraic

Ross L. Finney,… 5th Edition

Chapter 4, Problem 22

Instant Answer

Solved by Expert Adrian Co

08/28/2021

Step 1

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. Here, the outer function is $u^2$ and the inner function is $1+\cos 2x$. So we have: $$\frac{dy}{dx} = 2(1+\cos Show more…

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Find $d y / d x$. $$y=(1+\cos 2 x)^{2}$$

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Key Concepts

Chain Rule

A fundamental rule in calculus used to differentiate composite functions. When a function is applied within another function, the derivative of the outer function is evaluated at the inner function and multiplied by the derivative of the inner function.

Power Rule

A basic differentiation rule that states if a function is raised to a power, its derivative is the exponent multiplied by the original function raised to one less than that exponent. This rule is used in conjunction with the chain rule when the base of the exponent is a function of x.

Trigonometric Derivatives

Refers to the standard derivatives of trigonometric functions such as sine and cosine. In the context of composite functions, it is important to remember that the derivative of sine or cosine functions may require the multiplication by the derivative of the argument if it is itself a function of x.

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