Question

find the answer d/dx(sin 8x^2)

Answer 1

Let y = $\sin 8x^2$

We have to find, the value of $\dfrac{d}{dx} (\sin 8x^2)$.

Solution:

∴ y = $\sin 8x^2$

⇒ $\dfrac{dy}{dx}$ = $\dfrac{d}{dx}(\sin 8x^2)$

⇒ $\dfrac{dy}{dx}$ = $\cos 8x^2\dfrac{d}{dx}(8x^2)$ [ ∵ $\dfrac{d}{dx}(\sin x)=\cos x$]

⇒ $\dfrac{dy}{dx}$ = $\cos 8x^2(8.2x)$

⇒ $\dfrac{dy}{dx}$ = $16x\cos 8x^2$

∴ $\dfrac{d}{dx} (\sin 8x^2)$ = $16x\cos 8x^2$

Answer 2

Given :  sin (8x^2)

To Find : d/dx( sin (8x^2))

Solution:

d/dx( sin (8x^2))

= Cos(8x^2) d/dx  (8x^2)

= Cos(8x^2) * 8 d/dx  (x^2)

= Cos(8x^2)* 8 * 2x

= Cos(8x^2) * 16x

= 16xCos(8x^2)

d/dx( sin (8x^2))  = 16xCos(8x^2)

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