Question

If $\frac{d}{dx}f\left(x\right)=g\left(x\right)$, then $\frac{d}{dx}f(ax+b)=$______

Answer 1

Given,

$\frac{d}{dx}f\left(x\right)=g\left(x\right)$

or, $f^{\prime }\left(x\right)=g\left(x\right)$.......(1).

Now $\frac{d}{dx}f(ax+b)=f^{\prime }(ax+b).a=ag(ax+b).$ [ Using (1)]