Original Post: Y = squarerootx

Find the derivate of the function using the definition of derivate Y=squarerootx

Question

Original Post: Y = squarerootx

Find the derivate of the function using the definition of derivate Y=squarerootx

tkhunny · Answer

Wow!

mathmale · Answer

It appears to me that this question is both legitimate and complete.  Using a particular method, "the definition of the derivative," @lizzy92 is to find the derivative of $$y=\sqrt{x}$$

mathmale · Answer

The definition of the derivative of f(x) is as follows:$$f '(x) =limit~(as~h~approaches~zero)~of ~\frac{ f(x+h)-f(x) }{ h }$$

mathmale · Answer

Here, $$f(x)=\sqrt{x}~and~f(x+h)=\sqrt{x+h}$$

mathmale · Answer

lizzy:  what further help do you need at this point?

mathmale · Answer

@lizzy92:  ?

aum · Answer

$$
\lim_{h \rightarrow 0}\frac{\sqrt{x+h}-\sqrt{x}}{h} = ?
$$Multiply top and bottom by the conjugate of the numerator $\sqrt{x+h}+\sqrt{x}$ and simplify and then take the limit.

aum · Answer

Make use of the identity: $(a-b)(a+b) = a^2 - b^2$ after you multiply the numerator by its conjugate.

anonymous · Answer

Ok thank you guys! :)

aum · Answer

You are welcome.

anonymous · Answer

Thank you @mathmale :)