Question

Using the Chain rule find the derivative of the function: 1. y=(x?+2x2,6

Answer 1

Given function ,  $y=(x^{3}+2x^{2})^{6}$

Differentiating both side with respect to   we get ,

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

$\Rightarrow \frac{dy}{dx}=6(x^{3}+2x^{2})^{5}\frac{d}{dx}(x^{3}+2x^{2})$ , Using Chain rule .

$\Rightarrow \frac{dy}{dx}=6(x^{3}+2x^{2})^{5}\left \{ \frac{d}{dx}(x^{3})+2\frac{d}{dx}(x^{2}) \right \}$

$\Rightarrow \frac{dy}{dx}=6(x^{3}+2x^{2})^{5}(3x^{2}+4x)$

Hence ,

Answer :  $\frac{dy}{dx}=6(x^{3}+2x^{2})^{5}(3x^{2}+4x)$