Solve x^-3/2/frac{3{2}}

$$\frac { x ^ { - 3 / 2 } } { \frac { 3 } { 2 } }$$

Differentiate w.r.t. x

$$-\frac{1}{x^{\frac{5}{2}}}$$

Steps Using Definition of a Derivative

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

$$-\frac{3}{2}\times \frac{2}{3}x^{-\frac{3}{2}-1}$$

Multiply -\frac{3}{2} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$-x^{-\frac{3}{2}-1}$$

Subtract 1 from -\frac{3}{2}.

$$-x^{-\frac{5}{2}}$$

Evaluate

$$\frac{2}{3x^{\frac{3}{2}}}$$

Solution Steps

Divide x^{-\frac{3}{2}} by \frac{3}{2} by multiplying x^{-\frac{3}{2}} by the reciprocal of \frac{3}{2}.

$$\frac{x^{-\frac{3}{2}}\times 2}{3}$$