Resolver 10^-6*3^-7*625*t^-4

$$10 ^ { - 6 } \times 3 ^ { - 7 } \times 625 \times t ^ { - 4 }$$

Calcular

$$\frac{1}{3499200t^{4}}$$

Pasos da solución

Calcula 10 á potencia de -6 e obtén \frac{1}{1000000}.

$$\frac{1}{1000000}\times 3^{-7}\times 625t^{-4}$$

Calcula 3 á potencia de -7 e obtén \frac{1}{2187}.

$$\frac{1}{1000000}\times \frac{1}{2187}\times 625t^{-4}$$

Multiplica \frac{1}{1000000} e \frac{1}{2187} para obter \frac{1}{2187000000}.

$$\frac{1}{2187000000}\times 625t^{-4}$$

Multiplica \frac{1}{2187000000} e 625 para obter \frac{1}{3499200}.

$$\frac{1}{3499200}t^{-4}$$

Diferenciar w.r.t. t

$$-\frac{1}{874800t^{5}}$$

Pasos que usan a definición dunha derivada

Calcula 10 á potencia de -6 e obtén \frac{1}{1000000}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{1000000}\times 3^{-7}\times 625t^{-4})$$

Calcula 3 á potencia de -7 e obtén \frac{1}{2187}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{1000000}\times \frac{1}{2187}\times 625t^{-4})$$

Multiplica \frac{1}{1000000} e \frac{1}{2187} para obter \frac{1}{2187000000}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{2187000000}\times 625t^{-4})$$

Multiplica \frac{1}{2187000000} e 625 para obter \frac{1}{3499200}.

$$\frac{\mathrm{d}}{\mathrm{d}t}(\frac{1}{3499200}t^{-4})$$

A derivada de ax^{n} é nax^{n-1}.

$$-4\times \frac{1}{3499200}t^{-4-1}$$

Multiplica -4 por \frac{1}{3499200}.

$$-\frac{1}{874800}t^{-4-1}$$

Resta 1 de -4.

$$-\frac{1}{874800}t^{-5}$$