Solve 15x^1/5/3x^1/8

$$\frac { 15 x ^ { 1 / 5 } } { 3 x ^ { 1 / 8 } }$$

Evaluate

$$5x^{\frac{3}{40}}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{15^{1}\sqrt[5]{x}}{3^{1}\sqrt[8]{x}}$$

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

$$\frac{15^{1}x^{\frac{1}{5}-\frac{1}{8}}}{3^{1}}$$

Subtract \frac{1}{8} from \frac{1}{5} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\frac{15^{1}x^{\frac{3}{40}}}{3^{1}}$$

Divide 15 by 3.

$$5x^{\frac{3}{40}}$$

Differentiate w.r.t. x

$$\frac{3}{8x^{\frac{37}{40}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{15}{3}x^{\frac{1}{5}-\frac{1}{8}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{\frac{3}{40}})$$

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}.

$$\frac{3}{40}\times 5x^{\frac{3}{40}-1}$$

Do the arithmetic.

$$\frac{3}{8}x^{-\frac{37}{40}}$$