Solve frac{b^frac{3{2}}}{b^frac{-1{3}}}=

$$\frac { b ^ { \frac { 3 } { 2 } } } { b ^ { \frac { - 1 } { 3 } } } =$$

Differentiate w.r.t. b

$$\frac{11b^{\frac{5}{6}}}{6}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{\frac{3}{2}-\left(-\frac{1}{3}\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{\frac{11}{6}})$$

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}.

$$\frac{11}{6}b^{\frac{11}{6}-1}$$

Do the arithmetic.

$$\frac{11}{6}b^{\frac{5}{6}}$$

Evaluate

$$b^{\frac{11}{6}}$$