Solve (3/4b)(+2/3b)=

$$( 3 / 4 b ) ( + 2 / 3 b ) =$$

Evaluate

$$\frac{b^{2}}{2}$$

Solution Steps

Multiply b and b to get b^{2}.

$$\frac{3}{4}b^{2}\times \frac{2}{3}$$

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{3\times 2}{4\times 3}b^{2}$$

Cancel out 3 in both numerator and denominator.

$$\frac{2}{4}b^{2}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{1}{2}b^{2}$$

Differentiate w.r.t. b

$$b$$

Steps Using Definition of a Derivative

Multiply b and b to get b^{2}.

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

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Cancel out 3 in both numerator and denominator.

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

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{2}b^{2})$$

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

$$2\times \frac{1}{2}b^{2-1}$$

Multiply 2 times \frac{1}{2}.

$$b^{2-1}$$

Subtract 1 from 2.

$$b^{1}$$

For any term t, t^{1}=t.

$$b$$