Solve =frac{f(x_{0}+h)-f(x_{0})}{x_{0}+h-x_{0}}

$$= \frac { f ( x _ { 0 } + h ) - f ( x _ { 0 } ) } { x _ { 0 } + h - x _ { 0 } }$$

Evaluate

$$f$$

Short Solution Steps

Combine x_{0} and -x_{0} to get 0.

$$\frac{f\left(x_{0}+h\right)-fx_{0}}{h}$$

Factor the expressions that are not already factored.

$$\frac{fh}{h}$$

Cancel out h in both numerator and denominator.

$$f$$

Differentiate w.r.t. f

$$1$$

Steps Using Definition of a Derivative

Combine x_{0} and -x_{0} to get 0.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{f\left(x_{0}+h\right)-fx_{0}}{h})$$

Factor the expressions that are not already factored in \frac{f\left(x_{0}+h\right)-fx_{0}}{h}.

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

Cancel out h in both numerator and denominator.

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

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.

$$1$$