Solve 15b^9div3b^2

$$15 b ^ { 9 } \div 3 b ^ { 2 }$$

Evaluate

$$5b^{11}$$

Solution Steps

Divide 15b^{9} by 3 to get 5b^{9}.

$$5b^{9}b^{2}$$

To multiply powers of the same base, add their exponents. Add 9 and 2 to get 11.

$$5b^{11}$$

Differentiate w.r.t. b

$$55b^{10}$$

Steps Using Definition of a Derivative

Divide 15b^{9} by 3 to get 5b^{9}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(5b^{9}b^{2})$$

To multiply powers of the same base, add their exponents. Add 9 and 2 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}b}(5b^{11})$$

The derivative of ax^{n} is nax^{n-1}.

$$11\times 5b^{11-1}$$

Multiply 11 times 5.

$$55b^{11-1}$$

Subtract 1 from 11.

$$55b^{10}$$