Question

Find difference of the following with resoect to x

A) ${\left(x^3+6x^2+12x-13\right)}^{100}$

B) $\log \left(\sin \left(\log x\right)\right)$

Answer 1

(A) $\frac{d}{dx}{\left(x^3+6x^2+12x-13\right)}^{100}$.

$100{\left(x^3+6x^2+12x-12\right)}^{99}\left(3x^2+12x+12\right)$

$300\left(x^2+4x+4\right){\left(x^3+6x^2+12x-13\right)}^{99}$

(B) $\frac{d}{dx}\left(\log \sin \left(\log x\right)\right)$

$\frac{1}{\sin \left(\log x\right)}\times \cos \left(\log x\right)\times \frac{1}{2}$

$\frac{1}{x}$ $\frac{cos\left(logx\right)}{sin\left(logx\right)}$