Solve 24b^4div8b^2

$$24 b ^ { 4 } \div 8 b ^ { 2 }$$

Evaluate

$$3b^{6}$$

Solution Steps

Divide 24b^{4} by 8 to get 3b^{4}.

$$3b^{4}b^{2}$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$3b^{6}$$

Differentiate w.r.t. b

$$18b^{5}$$

Steps Using Definition of a Derivative

Divide 24b^{4} by 8 to get 3b^{4}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3b^{4}b^{2})$$

To multiply powers of the same base, add their exponents. Add 4 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3b^{6})$$

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

$$6\times 3b^{6-1}$$

Multiply 6 times 3.

$$18b^{6-1}$$

Subtract 1 from 6.

$$18b^{5}$$