Solve 9k+5k+3k+2k=

$$9 k + 5 k + 3 k + 2 k =$$

Evaluate

$$19k$$

Solution Steps

Combine 9k and 5k to get 14k.

$$14k+3k+2k$$

Combine 14k and 3k to get 17k.

$$17k+2k$$

Combine 17k and 2k to get 19k.

$$19k$$

Differentiate w.r.t. k

$$19$$

Steps Using Definition of a Derivative

Combine 9k and 5k to get 14k.

$$\frac{\mathrm{d}}{\mathrm{d}k}(14k+3k+2k)$$

Combine 14k and 3k to get 17k.

$$\frac{\mathrm{d}}{\mathrm{d}k}(17k+2k)$$

Combine 17k and 2k to get 19k.

$$\frac{\mathrm{d}}{\mathrm{d}k}(19k)$$

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

$$19k^{1-1}$$

Subtract 1 from 1.

$$19k^{0}$$

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

$$19\times 1$$

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

$$19$$