Solve v^frac{5{2}}divv^frac{1{2}}

$$v ^ { \frac { 5 } { 2 } } \div v ^ { \frac { 1 } { 2 } }$$

Evaluate

$$v^{2}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{v^{\frac{5}{2}}}{\sqrt{v}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$v^{\frac{5}{2}-\frac{1}{2}}$$

Subtract \frac{1}{2} from \frac{5}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$v^{2}$$

Differentiate w.r.t. v

$$2v$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}v}(\frac{1}{1}v^{\frac{5}{2}-\frac{1}{2}})$$

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2v^{2-1}$$

Do the arithmetic.

$$2v^{1}$$

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

$$2v$$