Solve 18x/5:9x^2/25

$$\frac { 18 x } { 5 } : \frac { 9 x ^ { 2 } } { 25 }$$

Evaluate

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

Solution Steps

Divide \frac{18x}{5} by \frac{9x^{2}}{25} by multiplying \frac{18x}{5} by the reciprocal of \frac{9x^{2}}{25}.

$$\frac{18x\times 25}{5\times 9x^{2}}$$

Cancel out 5\times 9x in both numerator and denominator.

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

Multiply 2 and 5 to get 10.

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

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Divide \frac{18x}{5} by \frac{9x^{2}}{25} by multiplying \frac{18x}{5} by the reciprocal of \frac{9x^{2}}{25}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18x\times 25}{5\times 9x^{2}})$$

Cancel out 5\times 9x in both numerator and denominator.

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

Multiply 2 and 5 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.

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