Solve 3f+f+05f

$$3 f + f + 05 f$$

Evaluate

$$4f$$

Solution Steps

Combine 3f and f to get 4f.

$$4f+0\times 5f$$

Multiply 0 and 5 to get 0.

$$4f+0f$$

Anything times zero gives zero.

$$4f+0$$

Anything plus zero gives itself.

$$4f$$

Differentiate w.r.t. f

$$4$$

Steps Using Definition of a Derivative

Combine 3f and f to get 4f.

$$\frac{\mathrm{d}}{\mathrm{d}f}(4f+0\times 5f)$$

Multiply 0 and 5 to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}f}(4f+0f)$$

Anything times zero gives zero.

$$\frac{\mathrm{d}}{\mathrm{d}f}(4f+0)$$

Anything plus zero gives itself.

$$\frac{\mathrm{d}}{\mathrm{d}f}(4f)$$

The derivative of ax^{n} is nax^{n-1}.

$$4f^{1-1}$$

Subtract 1 from 1.

$$4f^{0}$$

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

$$4\times 1$$

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

$$4$$