Solve 4x^frac{3{2}}div2x^frac{1{2}}

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

Evaluate

$$2x^{2}$$

Solution Steps

Divide 4x^{\frac{3}{2}} by 2 to get 2x^{\frac{3}{2}}.

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

To multiply powers of the same base, add their exponents. Add \frac{3}{2} and \frac{1}{2} to get 2.

$$2x^{2}$$

Differentiate w.r.t. x

$$4x$$

Steps Using Definition of a Derivative

Divide 4x^{\frac{3}{2}} by 2 to get 2x^{\frac{3}{2}}.

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

To multiply powers of the same base, add their exponents. Add \frac{3}{2} and \frac{1}{2} to get 2.

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

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

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

Multiply 2 times 2.

$$4x^{2-1}$$

Subtract 1 from 2.

$$4x^{1}$$

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

$$4x$$