Question

The derivative of sin x^2​

Answer 1

welcome to the concept of chain rule.

formula used

d(sinx) dx= cosx

and d(x^n) /dx= nx^n-1

and chain rule....

I hope my answer help you ✌️✌️.

mark answer as brainlist

Answer 2

Question:

The derivative of $sin\:{x}^{2}$

Solution:

Here,

y = $sin\:{x}^{2}$

By using Chain Rule

$\dfrac{d}{dx}(sin\:{x}^{2})$

$= cos\:{x}^{2}$

$= cos{x}^{2} .\: 2x$

$= 2x\:cos\:{x}^{2}$

So,

$\dfrac{dy}{dx} = 2x\:cos\:{x}^{2}$

Formulas used:

• $\dfrac{d}{dx}(sin \:x) = cos \:x$

• $\dfrac{d}{dy}({x}^{n}) = n{x}^{n-1}$