Solve 3f+f^2-f+3

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

Differentiate w.r.t. f

$$2\left(f+1\right)$$

Steps Using Derivative Rule for Sum

Combine 3f and -f to get 2f.

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

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}.

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

Subtract 1 from 1.

$$2f^{0}+2f^{2-1}$$

Subtract 1 from 2.

$$2f^{0}+2f^{1}$$

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

$$2f^{0}+2f$$

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

$$2\times 1+2f$$

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

$$2+2f$$

Evaluate

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

Solution Steps

Combine 3f and -f to get 2f.

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