Differentiate the following function with respect of `x : x^(-3)(5+3x)`

Answer

`frac{15}{x^{4}}-frac{6}{x^{3}`

Explanation

Differentiating the function with respect to x:
$$
\begin{aligned}
&\frac{d}{d x}\left(x^{-3}(5+3 x)\right)\\
&=\frac{d}{d x}\left(5 x^{-3}+3 x^{1-3}\right)\\
&=\frac{d}{d x}\left(5 x^{-3}+3 x^{-2}\right)\\
&=\frac{d}{d x}\left(5 x^{-3}\right)+\frac{d}{d x}\left(3 x^{-2}\right)\\
&=5 \frac{d}{d x}\left(x^{-3}\right)+3 \frac{d}{d x}\left(x^{-2}\right)\\
...