Question

What is the Derivative of : ( ax + b )ⁿ ?

Answer 1

$$\begin{gathered} \frac{d}{dx}{\left(ax+b\right)}^n=n{\left(ax+b\right)}^{n-1}\frac{d}{dx}\left(ax+b\right) \\ =n{\left(ax+b\right)}^{n-1}\left[\frac{d}{dx}\left(ax\right)+\frac{d}{dx}\left(b\right)\right] \\ =n{\left(ax+b\right)}^{n-1}\left[a+0\right] \\ =an{\left(ax+b\right)}^{n-1} \\ Hence,\frac{d}{dx}{\left(ax+b\right)}^n=an{\left(ax+b\right)}^{n-1} \end{gathered}$$