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anonymous
 one year ago
find the derivative of the function h(x)=sqrt(2x)
anonymous
 one year ago
find the derivative of the function h(x)=sqrt(2x)

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myininaya
 one year ago
Best ResponseYou've already chosen the best response.1by the sqrt( ) can be written as ( )^(1/2)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we are just in the first section and haven't learned the chain rule, and are required to use a longer method

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1ok the definition then

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[\lim_{h \rightarrow 0}\frac{f(x+h)f(x)}{h} =f'(x)\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1where we have f(x)=sqrt(2x) and so f(x+h)=sqrt(2(x+h)) <here just replaced my x's with (x+h)'s

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1sometimes a good method when you are trying to evaluate a limit algebraically and you have a difference/sum of radicals rationalizing might help

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1to rationalize recall conjugates

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1for example the conjugate of ab is a+b and the conjugate of a+b is ab

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1do you want to try to see what happens if you do the following: \[\lim_{h \rightarrow 0} \frac{\sqrt{2(x+h)}\sqrt{2x}}{h} \cdot \frac{\sqrt{2(x+h)}+\sqrt{2x}}{\sqrt{2(x+h)}+\sqrt{2x}}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right, I got it down to 1/sqrt2xh +sqrt2x

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1one sec let me check

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1that looks pretty sweet

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[\lim_{h \rightarrow 0}\frac{1}{\sqrt{2xh}+\sqrt{2x}}\]

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1your job is to just replace h with 0

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1any you could do a little magic afterwards to make the answer look a bit more tidy

myininaya
 one year ago
Best ResponseYou've already chosen the best response.1\[\frac{1}{2 \sqrt{2x}} \text{ is \right!} \]
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