Solve frac{x^frac{4{7}}}{x^frac{1{2}}}

$$\frac { x ^ { \frac { 4 } { 7 } } } { x ^ { \frac { 1 } { 2 } } }$$

Evaluate

$$\sqrt[14]{x}$$

Steps Using Quotient of Powers Property

Use the rules of exponents to simplify the expression.

$$\frac{x^{\frac{4}{7}}}{\sqrt{x}}$$

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

$$x^{\frac{4}{7}-\frac{1}{2}}$$

Subtract \frac{1}{2} from \frac{4}{7} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\sqrt[14]{x}$$

Differentiate w.r.t. x

$$\frac{1}{14x^{\frac{13}{14}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{\frac{4}{7}-\frac{1}{2}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\sqrt[14]{x})$$

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}.

$$\frac{1}{14}x^{\frac{1}{14}-1}$$

Do the arithmetic.

$$\frac{1}{14}x^{-\frac{13}{14}}$$