Question

Dada f(x) = $x^{3}$ e g(x) = f($x^{2}$) Encontre
a) f'(2)
b) g'(x)

Answer 1

Resposta:

a) f(x)=x^3

f'(x)=3x^2

b) f(x^2)=(x^2)^3=x^6

f(x^2)=x^6

g(x)=f(x^2)

g(x)=(x^2)^3=x^6

g(x)=x^6

g'(x)=6x^5

BONS ESTUDOS!

Answer 2

Explicação passo-a-passo:

a)

$\sf f(x)=x^3$

$\sf f'(x)=3x^{3-1}$

$\sf f'(x)=3x^2$

Logo:

$\sf f'(2)=3\cdot2^2$

$\sf f'(2)=3\cdot4$

$\sf \red{f'(2)=12}$

b)

$\sf g(x)=f(x^2)$

$\sf g(x)=(x^2)^3$

$\sf g(x)=x^{2\cdot3}$

$\sf g(x)=x^6$

Logo:

$\sf g'(x)=6x^{6-1}$

$\sf \red{g'(x)=6x^5}$