Solve 5/6A/frac{1{3}}

$$\frac { \frac { 5 } { 6 } A } { \frac { 1 } { 3 } }$$

Evaluate

$$\frac{5A}{2}$$

Solution Steps

Divide \frac{5}{6}A by \frac{1}{3} by multiplying \frac{5}{6}A by the reciprocal of \frac{1}{3}.

$$\frac{5}{6}A\times 3$$

Express \frac{5}{6}\times 3 as a single fraction.

$$\frac{5\times 3}{6}A$$

Multiply 5 and 3 to get 15.

$$\frac{15}{6}A$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{5}{2}A$$

Differentiate w.r.t. A

$$\frac{5}{2} = 2\frac{1}{2} = 2.5$$

Steps Using Definition of a Derivative

Divide \frac{5}{6}A by \frac{1}{3} by multiplying \frac{5}{6}A by the reciprocal of \frac{1}{3}.

$$\frac{\mathrm{d}}{\mathrm{d}A}(\frac{5}{6}A\times 3)$$

Express \frac{5}{6}\times 3 as a single fraction.

$$\frac{\mathrm{d}}{\mathrm{d}A}(\frac{5\times 3}{6}A)$$

Multiply 5 and 3 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}A}(\frac{15}{6}A)$$

Reduce the fraction \frac{15}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\mathrm{d}}{\mathrm{d}A}(\frac{5}{2}A)$$

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

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

Subtract 1 from 1.

$$\frac{5}{2}A^{0}$$

For any term t except 0, t^{0}=1.

$$\frac{5}{2}\times 1$$

For any term t, t\times 1=t and 1t=t.

$$\frac{5}{2}$$