Solve f+g(0)

$$f + g ( 0 )$$

Evaluate

$$f$$

Solution Steps

Anything times zero gives zero.

$$f+0$$

Anything plus zero gives itself.

$$f$$

Differentiate w.r.t. f

$$1$$

Steps Using Definition of a Derivative

Anything times zero gives zero.

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

Anything plus zero gives itself.

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

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

$$f^{1-1}$$

Subtract 1 from 1.

$$f^{0}$$

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

$$1$$