Solve (a)9^frac{3{2}}

$$( a ) 9 ^ { \frac { 3 } { 2 } }$$

Differentiate w.r.t. a

$$27$$

Steps Using Definition of a Derivative

Calculate 9 to the power of \frac{3}{2} and get 27.

$$\frac{\mathrm{d}}{\mathrm{d}a}(a\times 27)$$

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

$$27a^{1-1}$$

Subtract 1 from 1.

$$27a^{0}$$

For any term t except 0, t^{0}=1.

$$27\times 1$$

For any term t, t\times 1=t and 1t=t.

$$27$$

Evaluate

$$27a$$

Solution Steps

Calculate 9 to the power of \frac{3}{2} and get 27.

$$a\times 27$$