Solve 2/5*1000/x

$$\frac { 2 } { 5 } \times \frac { 1000 } { x }$$

Evaluate

$$\frac{400}{x}$$

Solution Steps

Multiply \frac{2}{5} times \frac{1000}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1000}{5x}$$

Cancel out 5 in both numerator and denominator.

$$\frac{2\times 200}{x}$$

Multiply 2 and 200 to get 400.

$$\frac{400}{x}$$

Differentiate w.r.t. x

$$-\frac{400}{x^{2}}$$

Steps Using Definition of a Derivative

Multiply \frac{2}{5} times \frac{1000}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 1000}{5x})$$

Cancel out 5 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{2\times 200}{x})$$

Multiply 2 and 200 to get 400.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{400}{x})$$

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

$$-400x^{-1-1}$$

Subtract 1 from -1.

$$-400x^{-2}$$