Solve 3/2xdiv1/16

$$\frac { 3 } { 2 x } \div \frac { 1 } { 16 }$$

Evaluate

$$\frac{24}{x}$$

Solution Steps

Divide \frac{3}{2x} by \frac{1}{16} by multiplying \frac{3}{2x} by the reciprocal of \frac{1}{16}.

$$\frac{3\times 16}{2x}$$

Cancel out 2 in both numerator and denominator.

$$\frac{3\times 8}{x}$$

Multiply 3 and 8 to get 24.

$$\frac{24}{x}$$

Differentiate w.r.t. x

$$-\frac{24}{x^{2}}$$

Steps Using Definition of a Derivative

Divide \frac{3}{2x} by \frac{1}{16} by multiplying \frac{3}{2x} by the reciprocal of \frac{1}{16}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 16}{2x})$$

Cancel out 2 in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3\times 8}{x})$$

Multiply 3 and 8 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{24}{x})$$

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

$$-24x^{-1-1}$$

Subtract 1 from -1.

$$-24x^{-2}$$