Solve 6c-7+11c-c+2

$$6 c - 7 + 11 c - c + 2$$

Evaluate

$$16c-5$$

Solution Steps

Combine 6c and 11c to get 17c.

$$17c-7-c+2$$

Combine 17c and -c to get 16c.

$$16c-7+2$$

Add -7 and 2 to get -5.

$$16c-5$$

Differentiate w.r.t. c

$$16$$

Steps Using Derivative Rule for Sum

Combine 6c and 11c to get 17c.

$$\frac{\mathrm{d}}{\mathrm{d}c}(17c-7-c+2)$$

Combine 17c and -c to get 16c.

$$\frac{\mathrm{d}}{\mathrm{d}c}(16c-7+2)$$

Add -7 and 2 to get -5.

$$\frac{\mathrm{d}}{\mathrm{d}c}(16c-5)$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$16c^{1-1}$$

Subtract 1 from 1.

$$16c^{0}$$

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

$$16\times 1$$

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

$$16$$