Solve frac{4n^frac{3{2}}}{4n^frac{1{2}}}

$$\frac { 4 n ^ { \frac { 3 } { 2 } } } { 4 n ^ { \frac { 1 } { 2 } } }$$

Evaluate

$$n$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{4^{1}n^{\frac{3}{2}}}{4^{1}\sqrt{n}}$$

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

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

Subtract 1 from 1.

$$4^{0}n^{\frac{3}{2}-\frac{1}{2}}$$

For any number a except 0, a^{0}=1.

$$n^{\frac{3}{2}-\frac{1}{2}}$$

Subtract \frac{1}{2} from \frac{3}{2} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$n^{1}$$

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

$$n$$

Differentiate w.r.t. n

$$1$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(\frac{4}{4}n^{\frac{3}{2}-\frac{1}{2}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}n}(n^{1})$$

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}.

$$n^{1-1}$$

Do the arithmetic.

$$n^{0}$$

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

$$1$$