Solve 12a^2b^3b^2b/4a^2b

$$\frac { 12 a ^ { 2 } b ^ { 3 } b ^ { 2 } b } { 4 a ^ { 2 } b }$$

Evaluate

$$3b^{5}$$

Solution Steps

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

$$\frac{12a^{2}b^{5}b}{4a^{2}b}$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{12a^{2}b^{6}}{4a^{2}b}$$

Cancel out 4ba^{2} in both numerator and denominator.

$$3b^{5}$$

Differentiate w.r.t. b

$$15b^{4}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{12a^{2}b^{5}b}{4a^{2}b})$$

To multiply powers of the same base, add their exponents. Add 5 and 1 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{12a^{2}b^{6}}{4a^{2}b})$$

Cancel out 4ba^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(3b^{5})$$

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

$$5\times 3b^{5-1}$$

Multiply 5 times 3.

$$15b^{5-1}$$

Subtract 1 from 5.

$$15b^{4}$$