How would I use the definition of the derivative to find (2/(sqrt(x))' ?

Question

anonymous · Answer

definition of a derivative, from first principles:
$$df/dx = \lim_{h \rightarrow 0}[f(x+h) - f(x)]/h$$$$d(2x^{-1/2})/dx = \lim_{h \rightarrow 0}(1/h)(1/\sqrt{x+h} - 1/\sqrt x)$$
next step is to add the fraction
when you add the fraction, rationalise the NUMERATOR by multiplying by the conugate
the x's drop out, then the h cancels with 1/h & it's downhill from there
If you need more explicit help, say so.

The trick is rationalising the numerator to be able to cancel out h's

anonymous · Answer

typos = multiply by the CONJUGATE

anonymous · Answer

Jashcache do you want me to write it out? or do you follow his comment?

anonymous · Answer

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