Solve frac{a^-frac{1{2}}}{1/2}

$$\frac { a ^ { - \frac { 1 } { 2 } } } { 1 / 2 }$$

Differentiate w.r.t. a

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

Steps Using Definition of a Derivative

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

$$-\frac{1}{2}\times 2a^{-\frac{1}{2}-1}$$

Multiply -\frac{1}{2} times 2.

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

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

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

Evaluate

$$\frac{2}{\sqrt{a}}$$

Solution Steps

Divide a^{-\frac{1}{2}} by \frac{1}{2} by multiplying a^{-\frac{1}{2}} by the reciprocal of \frac{1}{2}.

$$a^{-\frac{1}{2}}\times 2$$