Question

Derivative of $f\left(x\right)=\cos \left(x^2\right)$ is

• A. $-\left(2x\right)\sin \left(x^2\right)$
• B. $\left(2x\right)\sin \left(x^2\right)$
• C. $-\left(x^2\right)\sin \left(x^2\right)$
• D. $\left(x^2\right)\sin \left(x^2\right)$

Answer 1

Answer: (A)

Step 1: Given

$f\left(x\right)=\cos \left(x^2\right)$

Step 2: Formula used

$\frac{d\left(cosy\right)}{dy}=-siny$

$\frac{d\left(y^2\right)}{dy}=2y$

Step 3: Finding the derivative

The derivative of the function is

$\frac{df\left(x\right)}{dx}=\frac{d\cos \left(x^2\right)}{dx}$
Using chain rule we have

multiply and divide with $d\left(x^2\right)$,

$\frac{d\cos \left(x^2\right)}{d\left(x^2\right)}\times \frac{d\left(x^2\right)}{dx}$
=$-2x\left(sin{x}^2\right)$

Hence, derivative of $cos\left(x^2\right)$ = $-2x\left(sin{x}^2\right)$.