Resolver (8x)^frac{5{3}}

$$( 8 x ) ^ { \frac { 5 } { 3 } }$$

Calcular

$$32x^{\frac{5}{3}}$$

Pasos da solución

Expande \left(8x\right)^{\frac{5}{3}}.

$$8^{\frac{5}{3}}x^{\frac{5}{3}}$$

Calcula 8 á potencia de \frac{5}{3} e obtén 32.

$$32x^{\frac{5}{3}}$$

Diferenciar w.r.t. x

$$\frac{160x^{\frac{2}{3}}}{3}$$

Pasos que usan a definición dunha derivada

Expande \left(8x\right)^{\frac{5}{3}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8^{\frac{5}{3}}x^{\frac{5}{3}})$$

Calcula 8 á potencia de \frac{5}{3} e obtén 32.

$$\frac{\mathrm{d}}{\mathrm{d}x}(32x^{\frac{5}{3}})$$

A derivada de ax^{n} é nax^{n-1}.

$$\frac{5}{3}\times 32x^{\frac{5}{3}-1}$$

Multiplica \frac{5}{3} por 32.

$$\frac{160}{3}x^{\frac{5}{3}-1}$$

Resta 1 de \frac{5}{3}.

$$\frac{160}{3}x^{\frac{2}{3}}$$