Solve 8k+4k+2k-5k=

$$8 k + 4 k + 2 k - 5 k =$$

Evaluate

$$9k$$

Solution Steps

Combine 8k and 4k to get 12k.

$$12k+2k-5k$$

Combine 12k and 2k to get 14k.

$$14k-5k$$

Combine 14k and -5k to get 9k.

$$9k$$

Differentiate w.r.t. k

$$9$$

Steps Using Definition of a Derivative

Combine 8k and 4k to get 12k.

$$\frac{\mathrm{d}}{\mathrm{d}k}(12k+2k-5k)$$

Combine 12k and 2k to get 14k.

$$\frac{\mathrm{d}}{\mathrm{d}k}(14k-5k)$$

Combine 14k and -5k to get 9k.

$$\frac{\mathrm{d}}{\mathrm{d}k}(9k)$$

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

$$9k^{1-1}$$

Subtract 1 from 1.

$$9k^{0}$$

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

$$9\times 1$$

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

$$9$$