Derivative of y = x+sqrt(x) using definition of derivative.

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Sep 1st 2010, 02:13 PM
sdh2106

Derivative of y = x+sqrt(x) using definition of derivative.

Can someone help me find the derivative of f(x)=x+sqrt(x) using f'(x)=lim--> 0 [f(x+h)-f(h)/h]?

Thanks!
Sep 1st 2010, 02:24 PM
pickslides

$\displaystyle\lim_{x\to 0} \frac{f(x+h)-f(x)}{h}= \lim_{x\to 0} \frac{((x+h)+\sqrt{x+h})-(x+\sqrt{x})}{h}$

What next?
Sep 1st 2010, 02:29 PM
sdh2106

i got it from here (after some algebra and conjugate multiplication). i was reading the definition of the derivative wrong... its should have been -f(x) not -f(h). Thanks for the help!

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