Question

DERIVADAS
1. Encontre a derivada mediante a Regra da Cadeia:
a) (5x⁶ +2x³)⁴

Answer 1

a)

$\frac{d}{dx} ((5 {x}^{6} + 2 {x}^{3} ) {}^{4} ) \\ \\ 4 \times (5 {x}^{6} + 2 {x}^{3} ) {}^{4 - 1} \times \frac{d}{dx} ( {5x}^{6} + 2 {x}^{3} ) \\ \\ 4(5 {x}^{6} + 2 {x}^{3} ) {}^{3} \times 6 \times 5 {x}^{6 - 1} + 3 \times 2 {x}^{3 - 1} \\ \\ 4(5 {x}^{6} + 2 {x}^{3} ) {}^{3} \times 30 {x}^{5} + 6 {x}^{2} \\ \\ 4(30 {x}^{5} + 6 {x}^{2} )(5 {x}^{6} + 2 {x}^{3} ) {}^{3} \\ \\ (120 {x}^{5} + 24 {x}^{2} )(5 {x}^{6} + 2 {x}^{2} ){}^{3}$

Bons Estudos!