In Exercise, use limits to compute f′(x) [Hint: In Exercise, use the rationalization trick of Example.]
f(x) =
Example
Derivative of a Function with a Radical Find the derivative of f(x) = x > 0.
SOLUTION In simplifying the difference quotient, we use the algebraic identity (a + b)(a − b) = a2 − b2. So,
Sometimes, we can use our knowledge of differentiation to evaluate some difficult limits. Here is one illustration.
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