Precalculus Examples
f(x)=xf(x)=x , x=0x=0
Step 1
Consider the difference quotient formula.
f(x+h)-f(x)hf(x+h)−f(x)h
Step 2
Step 2.1
Evaluate the function at x=x+hx=x+h.
Step 2.1.1
Replace the variable xx with x+hx+h in the expression.
f(x+h)=x+hf(x+h)=x+h
Step 2.1.2
Simplify the result.
Step 2.1.2.1
Remove parentheses.
f(x+h)=x+hf(x+h)=x+h
Step 2.1.2.2
The final answer is x+hx+h.
x+hx+h
x+hx+h
x+hx+h
Step 2.2
Find the components of the definition.
f(x+h)=x+hf(x+h)=x+h
f(x)=xf(x)=x
f(x+h)=x+hf(x+h)=x+h
f(x)=xf(x)=x
Step 3
Plug in the components.
f(x+h)-f(x)h=x+h-(x)hf(x+h)−f(x)h=x+h−(x)h
Step 4
Step 4.1
Simplify the numerator.
Step 4.1.1
Subtract xx from xx.
h+0hh+0h
Step 4.1.2
Add hh and 00.
hhhh
hhhh
Step 4.2
Cancel the common factor of hh.
Step 4.2.1
Cancel the common factor.
hh
Step 4.2.2
Rewrite the expression.
1
1
1
Step 5
