Question

If $f\left(x\right)=x^n$

and f '(1) = 15, then the value of n is

Answer 1

We have,
$f\left(x\right)=x^n\mathrm{Differentiating}\mathrm{both}\mathrm{sides}w.r.t.x,\Rightarrow f\text{'}\left(x\right)={\mathrm{nx}}^{n-1}.\mathrm{Putting}x=1,\mathrm{we}\mathrm{get}f\text{'}\left(1\right)=n\Rightarrow n=15$