Solve x^2b^2divx^2b^3

$$x ^ { 2 } b ^ { 2 } \div x ^ { 2 } b ^ { 3 }$$

Evaluate

$$b^{5}$$

Solution Steps

Cancel out x^{2} in both numerator and denominator.

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

$$b^{5}$$

Differentiate w.r.t. b

$$5b^{4}$$

Steps Using Definition of a Derivative

Cancel out x^{2} in both numerator and denominator.

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

To multiply powers of the same base, add their exponents. Add 2 and 3 to get 5.

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

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

$$5b^{5-1}$$

Subtract 1 from 5.

$$5b^{4}$$