Solve (8f^2+2)+(9f^2+f+1)

$$( 8 f ^ { 2 } + 2 ) + ( 9 f ^ { 2 } + f + 1 )$$

Evaluate

$$17f^{2}+f+3$$

Solution Steps

Combine 8f^{2} and 9f^{2} to get 17f^{2}.

$$17f^{2}+2+f+1$$

Add 2 and 1 to get 3.

$$17f^{2}+3+f$$

Differentiate w.r.t. f

$$34f+1$$

Steps Using Derivative Rule for Sum

Combine 8f^{2} and 9f^{2} to get 17f^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}f}(17f^{2}+2+f+1)$$

Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}f}(17f^{2}+3+f)$$

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}.

$$2\times 17f^{2-1}+f^{1-1}$$

Multiply 2 times 17.

$$34f^{2-1}+f^{1-1}$$

Subtract 1 from 2.

$$34f^{1}+f^{1-1}$$

Subtract 1 from 1.

$$34f^{1}+f^{0}$$

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

$$34f+f^{0}$$

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

$$34f+1$$