Question

Calcule a derivada das funções compostas abaixo:
g) f(x)= (x^2 - 1)^3
h) f(x)= (x^4 - 3x^2 + 1)^2
j) f(x)= ^3√4t+1
k) f(x)=√1-x^2

Answer 1

G)
$f(x) = (x^{2} - 1)^{3}$

$f'(x) = 3 (x^{2} - 1)^{2} . 2x$

$6x . (x^{2}- 1)^{2}$

H

$f(x) = ( x^{4} - 3 x^{2} +1)^{2}$
 
$f'(x) = 2. ( x^{4} - 3 x^{2} +1) . ( 4 x^{3} - 6x)$

J

$f(t) = \sqrt[3]{4t + 1} = (4t + 1) ^\frac{1}{3}$

$\frac{1}{3} . (4t + 1) ^\frac{-2}{3} . 4$

$\frac{4}{3. \sqrt[3]{(4t + 1)^2} }$


K

$\sqrt[2]{1 - x^{2}} = (1 - x^{2} ) ^\frac{1}{2}$

$\frac{1}{2} . \frac{1}{(1 - x^{2} )^2} . 2x$

$f'(x) = \frac{x}{ \sqrt[2]{1 - x^{2} } }$