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

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

Calcula

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

Passos de solució

Multipliqueu x per x per obtenir x^{2}.

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

Calculeu 10 elevat a -11 per obtenir \frac{1}{100000000000}.

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

Multipliqueu -667 per \frac{1}{100000000000} per obtenir -\frac{667}{100000000000}.

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

Anul·leu 3 tant al numerador com al denominador.

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

Calculeu 10 elevat a 8 per obtenir 100000000.

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

Multipliqueu 5 per 100000000 per obtenir 500000000.

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

Dividiu 6x^{2} entre 500000000 per obtenir \frac{3}{250000000}x^{2}.

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

Multipliqueu -\frac{667}{100000000000} per \frac{3}{250000000} per obtenir -\frac{2001}{25000000000000000000}.

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

Diferencieu x

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

Passos per utilitzar la definició d'una derivada

Multipliqueu x per x per obtenir x^{2}.

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

Calculeu 10 elevat a -11 per obtenir \frac{1}{100000000000}.

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

Multipliqueu -667 per \frac{1}{100000000000} per obtenir -\frac{667}{100000000000}.

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

Anul·leu 3 tant al numerador com al denominador.

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

Calculeu 10 elevat a 8 per obtenir 100000000.

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

Multipliqueu 5 per 100000000 per obtenir 500000000.

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

Dividiu 6x^{2} entre 500000000 per obtenir \frac{3}{250000000}x^{2}.

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

Multipliqueu -\frac{667}{100000000000} per \frac{3}{250000000} per obtenir -\frac{2001}{25000000000000000000}.

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

La derivada de ax^{n} és nax^{n-1}.

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

Multipliqueu 2 per -\frac{2001}{25000000000000000000}.

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

Resteu 1 de 2.

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

Per a qualsevol terme t, t^{1}=t.

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