Solve (4x)^frac{3{2}}

$$( 4 x ) ^ { \frac { 3 } { 2 } }$$

Evaluate

$$8x^{\frac{3}{2}}$$

Solution Steps

Expand \left(4x\right)^{\frac{3}{2}}.

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

Calculate 4 to the power of \frac{3}{2} and get 8.

$$8x^{\frac{3}{2}}$$

Differentiate w.r.t. x

$$12\sqrt{x}$$

Steps Using Definition of a Derivative

Expand \left(4x\right)^{\frac{3}{2}}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4^{\frac{3}{2}}x^{\frac{3}{2}})$$

Calculate 4 to the power of \frac{3}{2} and get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{\frac{3}{2}})$$

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

$$\frac{3}{2}\times 8x^{\frac{3}{2}-1}$$

Multiply \frac{3}{2} times 8.

$$12x^{\frac{3}{2}-1}$$

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

$$12\sqrt{x}$$