Solve ab/cdivb/ac

$$\frac { a b } { c } \div \frac { b } { a c }$$

Evaluate

$$a^{2}$$

Solution Steps

Divide \frac{ab}{c} by \frac{b}{ac} by multiplying \frac{ab}{c} by the reciprocal of \frac{b}{ac}.

$$\frac{abac}{cb}$$

Cancel out bc in both numerator and denominator.

$$aa$$

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

$$a^{2}$$

Differentiate w.r.t. a

$$2a$$

Steps Using Definition of a Derivative

Divide \frac{ab}{c} by \frac{b}{ac} by multiplying \frac{ab}{c} by the reciprocal of \frac{b}{ac}.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{abac}{cb})$$

Cancel out bc in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}a}(aa)$$

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

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

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

$$2a^{2-1}$$

Subtract 1 from 2.

$$2a^{1}$$

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

$$2a$$