Solve b^-frac{11{4}}divb^-frac{1{2}}

$$b ^ { - \frac { 11 } { 4 } } \div b ^ { - \frac { 1 } { 2 } }$$

Differentiate w.r.t. b

$$-\frac{9}{4b^{\frac{13}{4}}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{-\frac{11}{4}-\left(-\frac{1}{2}\right)})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}b}(b^{-\frac{9}{4}})$$

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}.

$$-\frac{9}{4}b^{-\frac{9}{4}-1}$$

Do the arithmetic.

$$-\frac{9}{4}b^{-\frac{13}{4}}$$

Evaluate

$$\frac{1}{b^{\frac{9}{4}}}$$