Solve 5/x*2

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

Evaluate

$$\frac{10}{x}$$

Solution Steps

Express \frac{5}{x}\times 2 as a single fraction.

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

Multiply 5 and 2 to get 10.

$$\frac{10}{x}$$

Differentiate w.r.t. x

$$-\frac{10}{x^{2}}$$

Steps Using Definition of a Derivative

Express \frac{5}{x}\times 2 as a single fraction.

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

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{10}{x})$$

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

$$-10x^{-1-1}$$

Subtract 1 from -1.

$$-10x^{-2}$$