Solve ({x}^frac{3{2}}){left(1/2right)}^

$$( { x }^{ \frac{ 3 }{ 2 } } ) { \left( \frac{ 1 }{ 2 } \right) }^{ }$$

Differentiate w.r.t. x

$$\frac{3\sqrt{x}}{4}$$

Steps Using Definition of a Derivative

Calculate \frac{1}{2} to the power of 1 and get \frac{1}{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{\frac{3}{2}}\times \frac{1}{2})$$

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

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

Multiply \frac{3}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator. Then reduce the fraction to lowest terms if possible.

$$\frac{3}{4}x^{\frac{3}{2}-1}$$

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

$$\frac{3}{4}\sqrt{x}$$

Evaluate

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

Solution Steps

Calculate \frac{1}{2} to the power of 1 and get \frac{1}{2}.

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