Solve 48b^1/3/12b^3/4

$$\frac { 48 b ^ { 1 / 3 } } { 12 b ^ { 3 / 4 } }$$

Evaluate

$$\frac{4}{b^{\frac{5}{12}}}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{48^{1}\sqrt[3]{b}}{12^{1}b^{\frac{3}{4}}}$$

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

$$\frac{48^{1}b^{\frac{1}{3}-\frac{3}{4}}}{12^{1}}$$

Subtract \frac{3}{4} from \frac{1}{3} by finding a common denominator and subtracting the numerators. Then reduce the fraction to lowest terms if possible.

$$\frac{48^{1}b^{-\frac{5}{12}}}{12^{1}}$$

Divide 48 by 12.

$$4b^{-\frac{5}{12}}$$

Differentiate w.r.t. b

$$-\frac{5}{3b^{\frac{17}{12}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{48}{12}b^{\frac{1}{3}-\frac{3}{4}})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(4b^{-\frac{5}{12}})$$

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}.

$$-\frac{5}{12}\times 4b^{-\frac{5}{12}-1}$$

Do the arithmetic.

$$-\frac{5}{3}b^{-\frac{17}{12}}$$