Question

d/dx
(Sin ²(3x²+6) ​

Answer 1

Answer:

The answer is $6\sin(6x^2+12)$

Step-by-step explanation:

Let $y=\sin^2(3x^2+6)$

So using chain rule of differentiation,

$\frac{dy}{dx}=\frac{d}{dx}[\sin(3x^2+6)]^2=2\sin(3x^2+6)\times \cos(3x^2+6)\times (6x+0)$

     $=12x\sin(3x^2+6)\cos(3x^2+6)\\=6(2\sin(3x^2+6)\cos(3x^2+6))\\=6\sin(2(3x^2+6))\\=6\sin(6x^2+12)$, since $2\sin\theta\cos\theta=\sin2\theta$

Answer 2

It will be 2sin(3x^2+6)cos(3x^2+6)6x
= 6xsin(6x^2+12)