Solve k/3+k/6-k/9=

$$\frac { k } { 3 } + \frac { k } { 6 } - \frac { k } { 9 } =$$

Evaluate

$$\frac{7k}{18}$$

Solution Steps

Combine \frac{k}{3} and \frac{k}{6} to get \frac{1}{2}k.

$$\frac{1}{2}k-\frac{k}{9}$$

Combine \frac{1}{2}k and -\frac{k}{9} to get \frac{7}{18}k.

$$\frac{7}{18}k$$

Differentiate w.r.t. k

$$\frac{7}{18} = 0.3888888888888889$$

Steps Using Definition of a Derivative

Combine \frac{k}{3} and \frac{k}{6} to get \frac{1}{2}k.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{1}{2}k-\frac{k}{9})$$

Combine \frac{1}{2}k and -\frac{k}{9} to get \frac{7}{18}k.

$$\frac{\mathrm{d}}{\mathrm{d}k}(\frac{7}{18}k)$$

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

$$\frac{7}{18}k^{1-1}$$

Subtract 1 from 1.

$$\frac{7}{18}k^{0}$$

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

$$\frac{7}{18}\times 1$$

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

$$\frac{7}{18}$$