Question

Calcule as seguintes derivadas:

Answer 1

Derivada da potência

$f(x)={x}^{n}$

$\boxed{f'(x)=n{x}^{n-1}}$

a)$f(x)={x}^{12}$

$f'(x)=12{x}^{12-1}$

$\boxed{\boxed{f'(x)=12{x}^{11}}}$

b)$f(x)={x}^{21}$

$f'(x)=21{x}^{21-1}$

$\boxed{\boxed{f'(x)=21{x}^{20}}}$

c)$f(x)=\frac{-3}{{x}^{-9}}=-3{x}^{9}$

$f'(x)=-3.9{x}^{9-1}$

$\boxed{\boxed{f'(x)=-27{x}^{8}}}$

d) $f(x)=\frac{20}{{x}^{-20}}=20{x}^{20}$

$f'(x)=20{x}^{20-1}$

$\boxed{\boxed{f'(x)=20{x}^{19}}}$

e)$f(x)=11{x}^{8}$

$f'(x)=11.8{x}^{8-1}$

$\boxed{\boxed{f'(x)=88{x}^{7}}}$