# Derivative of a Function

Derivative using the limit formula

Plug in f(x) = 1/√x into the difference quotient f(x + h) - f(x) / h. Then plug in h = 0 into the final answer. I get 0/2√x, which is just 0. Is this correct?

### Comments for Derivative of a Function

 May 16, 2013 Derivative by: Staff Answer Part I The final answer is not 0. Since h = 0, the difference quotient f(x + h) - f(x) / h is undefined (you cannot divide by zero). However, as you have already pointed out, the derivative (or slope) of the function f(x) can be computed using the limit of the difference quotient as h → 0. f(x + h) - f(x) / h is the slope of a line passing through the two points (x, f(x)) and (x + h, f(x + h)). The slope at point (x, f(x)) is the limit of the difference quotient as h → 0. Substituting the function f(x) = 1/√x into the formula, it becomes: -------------------------------------------

 May 16, 2013 Derivative by: Staff ------------------------------------------- Part II To avoid dividing by 0 (when h = 0), the difference quotient just needs to be rearranged algebraically. Rationalize the numerator by multiplying by its conjugate -------------------------------------------

 May 16, 2013 Derivative by: Staff ------------------------------------------- Part III Factor out the h in the denominator, and then cancel with the h in the numerator. The rearranged (equivalent) fraction avoids the possibility of dividing by zero when h = 0. -------------------------------------------

 May 16, 2013 Derivative by: Staff ------------------------------------------- Part IV Replace h with 0, and then simplify the expression. Final Answer: Thanks for writing. Staff www.solving-math-problems.com