Question
Differentiate the following w.r.t. x :
$\frac{3}{5 \sqrt[3]{\left(2 x^2-7 x-5\right)^5}}$
$\frac{3}{5 \sqrt[3]{\left(2 x^2-7 x-5\right)^5}}$
Differentiating w.r.t. x, we get
$\begin{aligned} \frac{d y}{d x} & =\frac{3}{5} \frac{d}{d x}\left(2 x^2-7 x-5\right)^{-\frac{5}{3}} \\ & =\frac{3}{5} \times\left(-\frac{5}{3}\right)\left(2 x^2-7 x-5\right)^{-\frac{5}{3}-1} \cdot \frac{d}{d x}\left(2 x^2-7 x-5\right) \\ & =-\left(2 x^2-7 x-5\right)^{-\frac{8}{3}} \cdot(2 \times 2 x-7 \times 1-0) \\ & =-\frac{4 x-7}{\left(2 x^2-7 x-5\right)^{\frac{8}{3}}} \cdot\end{aligned}$
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