Differentiate the following with respect to x:

To Find: Differentiation

NOTE : When 2 functions are in the product then we used product rule i.e

$\frac{d(u \cdot v)}{d x}=v \frac{d u}{d x}+u \frac{d v}{d x}$

Formula used: $\frac{d}{d x}\left(y^{n}\right)=n y^{n-1} \times \frac{d y}{d x}$

Let us take $y=\frac{1}{\left(x^{2}-x+3\right)^{3}}=\left(x^{2}-x+3\right)^{-3}$

So, by using the above formula, we have

$\frac{d}{d x}\left(x^{2}-x+3\right)^{-3}=-3\left(x^{2}-x+3\right)^{-4} \times(2 x-1)=-3 \frac{1}{\left(x^{2}-x+3\right)^{-4}}(2 x-1)$

Differentiation of $y=\left(x^{2}-x+3\right)^{-3}$ is $\frac{-3(2 x-1)}{\left(x^{2}-x+3\right)^{-4}}$