Solve 5/k+20/k+60/k-4/k

$$\frac { 5 } { k } + \frac { 20 } { k } + \frac { 60 } { k } - \frac { 4 } { k }$$

Evaluate

$$\frac{81}{k}$$

Solution Steps

Since \frac{5}{k} and \frac{20}{k} have the same denominator, add them by adding their numerators. Add 5 and 20 to get 25.

$$\frac{25}{k}+\frac{60}{k}-\frac{4}{k}$$

Since \frac{25}{k} and \frac{60}{k} have the same denominator, add them by adding their numerators. Add 25 and 60 to get 85.

$$\frac{85}{k}-\frac{4}{k}$$

Since \frac{85}{k} and \frac{4}{k} have the same denominator, subtract them by subtracting their numerators. Subtract 4 from 85 to get 81.

$$\frac{81}{k}$$

Differentiate w.r.t. k

$$-\frac{81}{k^{2}}$$

Steps Using Definition of a Derivative

Since \frac{5}{k} and \frac{20}{k} have the same denominator, add them by adding their numerators. Add 5 and 20 to get 25.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{25}{k}+\frac{60}{k}-\frac{4}{k})$$

Since \frac{25}{k} and \frac{60}{k} have the same denominator, add them by adding their numerators. Add 25 and 60 to get 85.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{85}{k}-\frac{4}{k})$$

Since \frac{85}{k} and \frac{4}{k} have the same denominator, subtract them by subtracting their numerators. Subtract 4 from 85 to get 81.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{81}{k})$$

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

$$-81k^{-1-1}$$

Subtract 1 from -1.

$$-81k^{-2}$$