Solve b^9/b^-2

$$\frac { b ^ { 9 } } { b ^ { - 2 } }$$

Differentiate w.r.t. b

$$11b^{10}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{1}b^{9-\left(-2\right)})$$

Do the arithmetic.

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

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}.

$$11b^{11-1}$$

Do the arithmetic.

$$11b^{10}$$

Evaluate

$$b^{11}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract -2 from 9 to get 11.

$$b^{11}$$