Solve 1/3b*2/5b=

$$\frac { 1 } { 3 } b \cdot \frac { 2 } { 5 } b =$$

Evaluate

$$\frac{2b^{2}}{15}$$

Solution Steps

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

$$\frac{1}{3}b^{2}\times \frac{2}{5}$$

Multiply \frac{1}{3} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 2}{3\times 5}b^{2}$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 5}.

$$\frac{2}{15}b^{2}$$

Differentiate w.r.t. b

$$\frac{4b}{15}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1}{3}b^{2}\times \frac{2}{5})$$

Multiply \frac{1}{3} times \frac{2}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{1\times 2}{3\times 5}b^{2})$$

Do the multiplications in the fraction \frac{1\times 2}{3\times 5}.

$$\frac{\mathrm{d}}{\mathrm{d}b}(\frac{2}{15}b^{2})$$

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

$$2\times \frac{2}{15}b^{2-1}$$

Multiply 2 times \frac{2}{15}.

$$\frac{4}{15}b^{2-1}$$

Subtract 1 from 2.

$$\frac{4}{15}b^{1}$$

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

$$\frac{4}{15}b$$