Solve x^frac{4{2}-3/2}

$$x ^ { \frac { 4 } { 2 } - \frac { 3 } { 2 } }$$

Evaluate

$$\sqrt{x}$$

Solution Steps

Divide 4 by 2 to get 2.

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

Subtract \frac{3}{2} from 2 to get \frac{1}{2}.

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

Differentiate w.r.t. x

$$\frac{1}{2\sqrt{x}}$$

Steps Using Definition of a Derivative

Divide 4 by 2 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2-\frac{3}{2}})$$

Subtract \frac{3}{2} from 2 to get \frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{1}{2}})$$

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

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

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

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