Question

if y=(3x^2 + 2)^4 then find dy/dx​

Answer 1

Finding Derivatives

Before we solve the problem, let us know an essential formula of differentiation.

$\quad\frac{d}{dx}(x^{n})=n\:x^{n-1}$ where $n$ is an integer.

Now we solve the problem.

Given, $y=(3x^{2}+2)^{4}$

Differentiating both sides with respect to $x$ we get

$\quad \frac{dy}{dx}=\frac{dy}{dx}(3x^{2}+2)^{4}$

$\Rightarrow \frac{dy}{dx}=4\:(3x^{2}+2)^{4-1}\:\frac{d}{dx}(3x^{2}+4)$

$\Rightarrow \frac{dy}{dx}=4\:(3x^{2}+2)^{3}\:[\frac{d}{dx}(3x^{2})+\frac{d}{dx}(2)]$

$\Rightarrow \frac{dy}{dx}=4\:(3x^{2}+2)^{3}\:6x$

$\Rightarrow \frac{dy}{dx}=24\:x\:(3x^{2}+2)^{3}$

This is the required derivative.

Answer 2

Before we solve the problem, let us know an essential formula of differentiation.

where  is an integer.

Now we solve the problem.

Given,  

Differentiating both sides with respect to  we get

This is the required derivative