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Difference quotient for f(x)=1xf{\left(x \right)} = \frac{1}{x}

The calculator will find the difference quotient for the function f(x)=1xf{\left(x \right)} = \frac{1}{x}, with steps shown.

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Your Input

Find the difference quotient for f(x)=1xf{\left(x \right)} = \frac{1}{x}.

Solution

The difference quotient is given by f(x+h)−f(x)h\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h}.

To find f(x+h)f{\left(x + h \right)}, plug x+hx + h instead of xx: f(x+h)=1x+hf{\left(x + h \right)} = \frac{1}{x + h}.

Finally, f(x+h)−f(x)h=1x+h−1xh=−1x(h+x)\frac{f{\left(x + h \right)} - f{\left(x \right)}}{h} = \frac{\frac{1}{x + h} - \frac{1}{x}}{h} = - \frac{1}{x \left(h + x\right)}.

Answer

The difference quotient for f(x)=1xf{\left(x \right)} = \frac{1}{x}A is −1x(h+x)- \frac{1}{x \left(h + x\right)}A.