Solve 2ab/5div4b/a

$$\frac { 2 a b } { 5 } \div \frac { 4 b } { a }$$

Evaluate

$$\frac{a^{2}}{10}$$

Solution Steps

Divide \frac{2ab}{5} by \frac{4b}{a} by multiplying \frac{2ab}{5} by the reciprocal of \frac{4b}{a}.

$$\frac{2aba}{5\times 4b}$$

Cancel out 2b in both numerator and denominator.

$$\frac{aa}{2\times 5}$$

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

$$\frac{a^{2}}{2\times 5}$$

Multiply 2 and 5 to get 10.

$$\frac{a^{2}}{10}$$

Differentiate w.r.t. a

$$\frac{a}{5}$$

Steps Using Definition of a Derivative

Divide \frac{2ab}{5} by \frac{4b}{a} by multiplying \frac{2ab}{5} by the reciprocal of \frac{4b}{a}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{2aba}{5\times 4b})$$

Cancel out 2b in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{aa}{2\times 5})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}}{2\times 5})$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{a^{2}}{10})$$

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

$$2\times \frac{1}{10}a^{2-1}$$

Multiply 2 times \frac{1}{10}.

$$\frac{1}{5}a^{2-1}$$

Subtract 1 from 2.

$$\frac{1}{5}a^{1}$$

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

$$\frac{1}{5}a$$