Solve 9/2(a)^1/2-(7/2(a)^1/2)

$$9 / 2 ( a ) ^ { 1 / 2 } - ( 7 / 2 ( a ) ^ { 1 / 2 } )$$

Differentiate w.r.t. a

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

Steps Using Definition of a Derivative

Combine \frac{9}{2}a^{\frac{1}{2}} and -\frac{7}{2}a^{\frac{1}{2}} to get a^{\frac{1}{2}}.

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

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

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

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

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

Evaluate

$$\sqrt{a}$$

Solution Steps

Combine \frac{9}{2}a^{\frac{1}{2}} and -\frac{7}{2}a^{\frac{1}{2}} to get a^{\frac{1}{2}}.

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