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which is correct? i.e a+b\a-b (after rationallization)a+b\a-b * a+b\a+b or a+b\a-b * a-b\a-b ?
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Other answers:

can it be a-b rather than a+b?
it would be equal but it wouldn't helpful in rationalisation
all right thanks
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one more question ?
may i ask
yes!
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u got?
how will we use power rule in this question?
so the first step would be to remember that the the derivative of a sum , is the sum of derivatives
yes yes
\[\frac{\text d}{\text d x}(1+\sqrt{1-x^2})=\frac{\text d}{\text d x}(1)+\frac{\text d}{\text d x}\left(\sqrt{1-x^2}\right)\]
derivative of a constant will be 0
right
so the problem is much simpler now
can you remember the derivative of a function of a function?
to me it's start right now:)
i'm sorry
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\[ (f\circ g)'(x)=f(g(x))'=f'(g(x))g'(x)\]
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you have to multiply by the derivative of the the inside function
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following?
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yeah
but how?
\[\frac{\text d}{\text d x}(1+\sqrt{1-x^2})\]\[=\frac{\text d}{\text d x}(1)+\frac{\text d}{\text d x}\left(\sqrt{1-x^2}\right)\]\[=\frac{\text d}{\text d x}\left(\sqrt{1-x^2}\right)\] \[\qquad\frac{\text d}{\text dx}f(g(x))=(f\circ g)'(x)=g'(x)f'(g(x))\]\[\qquad f(x)= x^{1/2}\qquad f'(x)=\frac12x^{-1/2}\]\[\qquad g(x)=1-x^2\qquad g'(x)=-2x\] \[=-2x\times\frac12(1-x^2)^{-1/2}\]
i know this stuff is tricky, can you tell me where about you are having trouble
haha
it is but u have solved it thank u so much!!
yeah but do understand the chain rule/,
no will be tomorow in college
hey did you use chain rule?
the chain rule for the derivative of a function of a function \[(f\circ g)'(x)=g'(x)f'(g(x))\]
is there any other way for this question except chain rule?
u didt use power rule? did u?
i used the power fule to find f '(x) and g'((x)
confusing me
watch this video , skip the first 5 minutes http://www.khanacademy.org/math/calculus/differential-calculus/e/chain_rule_1
actually i have solved all my questions except this one in quite a simple way
did you get the right answers?
i'm solving questions using theorems
there is no video
yeah answer is right
well you will have to learn the chain rule
this is the link i ment http://www.khanacademy.org/math/calculus/differential-calculus/v/the-chain-rule?exid=chain_rule_1
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mistake* -2x\ 2 sqrt 1 - x square
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you can cancel the two
yeah rightly said!

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