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 $y=(5+7 x)^{6}$

So, by using the above formula, we have

$\frac{d}{d x}(5+7 x)^{6}=6(5+7 x)^{5} \times \frac{d}{d x}(5+7 x)=6(5+7 x)^{5} \times 7=42(5+7 x)^{5}$

Differentiation of $y=(5+7 x)^{6}$ is $42(5+7 x)^{5}$