Chapter 5.4, Problem 1QR

To determine

To find: derivative of the given equation.

Answer to Problem 1QR

  $\frac{dy}{dx}=2x\cos \left(x^2\right)$ .

Explanation of Solution

Given:

  $y=\sin \left(x^2\right)$ .

Formula used:

  $\begin{array}{l}\frac{d}{dx}\left(\sin x\right)=\cos x\\ \frac{d}{dx}\left(x^n\right)=n{x}^{n-1}\end{array}$

Calculation:

Consider the given equation,

  $y=\sin \left(x^2\right)$

Differentiating with respect to $x$ , it follows that

  $\begin{array}{c}\frac{dy}{dx}=\frac{d}{dx}\left[\sin \left(x^2\right)\right]\\ =\cos \left(x^2\right)\cdot \frac{d}{dx}\left(x^2\right)\\ =\cos \left(x^2\right)\cdot 2x\\ =2x\cos \left(x^2\right)\end{array}$