Chapter 2: Q. 6 (page 232)

Suppose you wish to differentiate $g (x) = \sin^{2} (x) + \cos^{2} (x)$ .What is the fastest way to do this, and why?

Short Answer

Expert verified

The fastest way is to use chain rule and derivates of trigonometric functions.

Step by step solution

Step 1. Given Information.

The given function is $g (x) = \sin^{2} (x) + \cos^{2} (x)$ .

Step 2. Derivative.

The easiest way to find the derivative is using chain rule and derivative of trigonometric functions.

That is,

$\frac{d}{d x} g (x) = \frac{d}{d x} (\sin^{2} (x) + \cos^{2} (x)) g^{'} (x) = \frac{d}{d x} \sin^{2} (x) + \frac{d}{d x} \cos^{2} (x) g^{'} (x) = 2 \sin x \frac{d}{d x} \sin (x) + 2 \cos x \frac{d}{d x} \cos (x) = 2 \sin x \cos x - 2 \cos x \sin x$

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Suppose you wish to differentiate $g (x) = \sin^{2} (x) + \cos^{2} (x)$ .What is the fastest way to do this, and why?

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Derivative.

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Suppose you wish to differentiateg(x)=sin2(x)+cos2(x).What is the fastest way to do this, and why?

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Derivative.

One App. One Place for Learning.

Most popular questions from this chapter

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Study anywhere. Anytime. Across all devices.

Suppose you wish to differentiate $g (x) = \sin^{2} (x) + \cos^{2} (x)$ .What is the fastest way to do this, and why?