Solve 5f^2+3+4f+f

$$5 f ^ { 2 } + 3 + 4 f + f$$

Differentiate w.r.t. f

$$10f+5$$

Steps Using Derivative Rule for Sum

Combine 4f and f to get 5f.

$$\frac{\mathrm{d}}{\mathrm{d}f}(5f^{2}+3+5f)$$

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}.

$$2\times 5f^{2-1}+5f^{1-1}$$

Multiply 2 times 5.

$$10f^{2-1}+5f^{1-1}$$

Subtract 1 from 2.

$$10f^{1}+5f^{1-1}$$

Subtract 1 from 1.

$$10f^{1}+5f^{0}$$

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

$$10f+5f^{0}$$

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

$$10f+5\times 1$$

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

$$10f+5$$

Evaluate

$$5f^{2}+5f+3$$

Solution Steps

Combine 4f and f to get 5f.

$$5f^{2}+3+5f$$