Question

Derivada de 2(x^4 - 4 )^5 + 6x³

Answer 1

f(x) = 2(x^4 - 4)^5 + 6x^3

Usar regra da Cadeia.

f´(x) = 5*2(x^4 - 4)^4 * (x^4 - 4)' + 3*6x²

f'(x) = 10(x^4 -4)^4 * 4x³ + 18x²

f'(x) = 40x³(x^4 - 4)^4 + 18x²

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17/02/2016 
Sepauto - SSRC
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Answer 2

Sabemos que a regra da cadeia:

$\large{\boxed{[fog(x)]' = f'(g(x))*g'(x)}$

E a regra do "tombo":

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

Então, temos que:

$f(x) = 2(x^4-4)^5+6x^3\\ \\ f'(x)=2\cdot~5(x^4-4)^4\cdot~4x^3+6\cdot3x^2\\ \\ \large\boxed{f'(x)=40x^3(x^4-4)^4+18x^2}$