Solve 4a^2b^2*2b^2/8a^2b

$$\frac { 4 a ^ { 2 } b ^ { 2 } \cdot 2 b ^ { 2 } } { 8 a ^ { 2 } b }$$

Evaluate

$$b^{3}$$

Solution Steps

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

$$\frac{4a^{2}b^{4}\times 2}{8a^{2}b}$$

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

$$b^{3}$$

Differentiate w.r.t. b

$$3b^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{4a^{2}b^{4}\times 2}{8a^{2}b})$$

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

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

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

$$3b^{3-1}$$

Subtract 1 from 3.

$$3b^{2}$$