Solve 12/a+5/a

$$1 \frac { 2 } { a } + \frac { 5 } { a }$$

Evaluate

$$\frac{7}{a}$$

Solution Steps

Express 1\times \frac{2}{a} as a single fraction.

$$\frac{2}{a}+\frac{5}{a}$$

Since \frac{2}{a} and \frac{5}{a} have the same denominator, add them by adding their numerators. Add 2 and 5 to get 7.

$$\frac{7}{a}$$

Differentiate w.r.t. a

$$-\frac{7}{a^{2}}$$

Steps Using Definition of a Derivative

Express 1\times \frac{2}{a} as a single fraction.

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

Since \frac{2}{a} and \frac{5}{a} have the same denominator, add them by adding their numerators. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}a}(\frac{7}{a})$$

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

$$-7a^{-1-1}$$

Subtract 1 from -1.

$$-7a^{-2}$$