Question

Find the second order derivatives of the function x^20

Answer 1

we know concept ,
if a function $y=f(x)^n$ is given
then $\frac{dy}{dx}=nf(x)^{(n-1)}\frac{df(x)}{dx}$ use this here,

given, $y=x^{20}$
now differentiate y with respect to x
$\frac{dy}{dx}=\frac{d(x^{20})}{dx}\\=20x^{20-1}=20x^{19}$
hence , 1st oder derivative is $\frac{dy}{dx}=20x^{19}$
for getting 2nd order derivatives of function, differentiate $\frac{dy}{dx}$ once again,
$\frac{d}{dx}(dy/dx)=20.19x^{19-1}=380x^{18}$

hence, $\frac{d^2y}{dx^2}=\bf{380x^{18}}$