Question

Find differential of the following with respect to x

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

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

Answer 1

It seems question has been wrongly formatted as a 'Multiple Choice Question'. It has two parts (A) and (B) for which differential has to be provided.

Also the part B seem to have a typographical error, it should read as

$\log \left[\sin (\log x)\right]$

Differential for A

$(x^3+6x^2+12x-13{)}^{100}$

Differentiating w.r.t. x

$\Rightarrow 100(x^3+6x^2+12x-13{)}^{99}+({3x}^2+12x+12)$

Differential for B

$\log \left[\sin (\log x)\right]$

Differentiating w.r.t. x

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