Solve (7c^2+8)+(3c+3)

$$( 7 c ^ { 2 } + 8 ) + ( 3 c + 3 )$$

Differentiate w.r.t. c

$$14c+3$$

Steps Using Derivative Rule for Sum

Add 8 and 3 to get 11.

$$\frac{\mathrm{d}}{\mathrm{d}c}(7c^{2}+11+3c)$$

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}.

$$2\times 7c^{2-1}+3c^{1-1}$$

Multiply 2 times 7.

$$14c^{2-1}+3c^{1-1}$$

Subtract 1 from 2.

$$14c^{1}+3c^{1-1}$$

Subtract 1 from 1.

$$14c^{1}+3c^{0}$$

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

$$14c+3c^{0}$$

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

$$14c+3\times 1$$

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

$$14c+3$$

Evaluate

$$7c^{2}+3c+11$$

Solution Steps

Add 8 and 3 to get 11.

$$7c^{2}+11+3c$$