Resolver -667*10^-1118x*x/15*10^8

$$-667 \times { 10 }^{ -11 } \frac{ 18x \times x }{ 15 \times { 10 }^{ 8 } }$$

Calcular

$$-\frac{2001x^{2}}{25000000000000000000}$$

Pasos da solución

Multiplica x e x para obter x^{2}.

$$-667\times 10^{-11}\times \frac{18x^{2}}{15\times 10^{8}}$$

Calcula 10 á potencia de -11 e obtén \frac{1}{100000000000}.

$$-667\times \frac{1}{100000000000}\times \frac{18x^{2}}{15\times 10^{8}}$$

Multiplica -667 e \frac{1}{100000000000} para obter -\frac{667}{100000000000}.

$$-\frac{667}{100000000000}\times \frac{18x^{2}}{15\times 10^{8}}$$

Anula 3 no numerador e no denominador.

$$-\frac{667}{100000000000}\times \frac{6x^{2}}{5\times 10^{8}}$$

Calcula 10 á potencia de 8 e obtén 100000000.

$$-\frac{667}{100000000000}\times \frac{6x^{2}}{5\times 100000000}$$

Multiplica 5 e 100000000 para obter 500000000.

$$-\frac{667}{100000000000}\times \frac{6x^{2}}{500000000}$$

Divide 6x^{2} entre 500000000 para obter \frac{3}{250000000}x^{2}.

$$-\frac{667}{100000000000}\times \frac{3}{250000000}x^{2}$$

Multiplica -\frac{667}{100000000000} e \frac{3}{250000000} para obter -\frac{2001}{25000000000000000000}.

$$-\frac{2001}{25000000000000000000}x^{2}$$

Diferenciar w.r.t. x

$$-\frac{2001x}{12500000000000000000}$$

Pasos que usan a definición dunha derivada

Multiplica x e x para obter x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-667\times 10^{-11}\times \frac{18x^{2}}{15\times 10^{8}})$$

Calcula 10 á potencia de -11 e obtén \frac{1}{100000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-667\times \frac{1}{100000000000}\times \frac{18x^{2}}{15\times 10^{8}})$$

Multiplica -667 e \frac{1}{100000000000} para obter -\frac{667}{100000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{667}{100000000000}\times \frac{18x^{2}}{15\times 10^{8}})$$

Anula 3 no numerador e no denominador.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{667}{100000000000}\times \frac{6x^{2}}{5\times 10^{8}})$$

Calcula 10 á potencia de 8 e obtén 100000000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{667}{100000000000}\times \frac{6x^{2}}{5\times 100000000})$$

Multiplica 5 e 100000000 para obter 500000000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{667}{100000000000}\times \frac{6x^{2}}{500000000})$$

Divide 6x^{2} entre 500000000 para obter \frac{3}{250000000}x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{667}{100000000000}\times \frac{3}{250000000}x^{2})$$

Multiplica -\frac{667}{100000000000} e \frac{3}{250000000} para obter -\frac{2001}{25000000000000000000}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-\frac{2001}{25000000000000000000}x^{2})$$

A derivada de ax^{n} é nax^{n-1}.

$$2\left(-\frac{2001}{25000000000000000000}\right)x^{2-1}$$

Multiplica 2 por -\frac{2001}{25000000000000000000}.

$$-\frac{2001}{12500000000000000000}x^{2-1}$$

Resta 1 de 2.

$$-\frac{2001}{12500000000000000000}x^{1}$$

Para calquera termo t, t^{1}=t.

$$-\frac{2001}{12500000000000000000}x$$