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

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

Evaluate

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

Solution Steps

Multiply x and x to get x^{2}.

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

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

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

Multiply -667 and \frac{1}{100000000000} to get -\frac{667}{100000000000}.

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

Cancel out 3 in both numerator and denominator.

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

Calculate 10 to the power of 8 and get 100000000.

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

Multiply 5 and 100000000 to get 500000000.

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

Divide 6x^{2} by 500000000 to get \frac{3}{250000000}x^{2}.

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

Multiply -\frac{667}{100000000000} and \frac{3}{250000000} to get -\frac{2001}{25000000000000000000}.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

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

Calculate 10 to the power of -11 and get \frac{1}{100000000000}.

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

Multiply -667 and \frac{1}{100000000000} to get -\frac{667}{100000000000}.

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

Cancel out 3 in both numerator and denominator.

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

Calculate 10 to the power of 8 and get 100000000.

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

Multiply 5 and 100000000 to get 500000000.

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

Divide 6x^{2} by 500000000 to get \frac{3}{250000000}x^{2}.

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

Multiply -\frac{667}{100000000000} and \frac{3}{250000000} to get -\frac{2001}{25000000000000000000}.

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

The derivative of ax^{n} is nax^{n-1}.

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

Multiply 2 times -\frac{2001}{25000000000000000000}.

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

Subtract 1 from 2.

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

For any term t, t^{1}=t.

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