krypton
inverse and inverse trignometric functions
find d/dx(arctan^2(sqrt(x))
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hsmt
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hi krypton.. you still there? I think i might be able to help if you are
krypton
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yea dear
hsmt
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consider the derivative of arctan^2(u) where u=sqrt x and use the chain rule...
hsmt
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sorry. let's start with the derivative of (tan-1u)^2. what is the derivative of this little beastie. lol there we go...
krypton
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u mean?
hsmt
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what is the derivative of (f(x))^2?
hsmt
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it would be something like 2(f(x))times f prime of x
hsmt
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in this case, f(u)=tan-1u, where u=sqrt of x. does this make sense?
hsmt
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questions are good here. the more you ask, the more i can help... :)
krypton
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yea
hsmt
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so what is the derivative of tan-1u?
hsmt
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you can give me your best guess if you like
krypton
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hmm actually i wasnt in the class when the topic was taught, but i thinkis =1/srt 1-x^2?
krypton
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sorry 1/1+x^2
hsmt
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that is totally correct. :) now replace the x with u so that we can use the chain rule where u=1/sqrtx.
krypton
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so thats the answer?
hsmt
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no, we have a power of tan-1. so the answer is 2(tan-1(sqrtx))(1/(1+x))1/2sqrtx
hsmt
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is that making sense to you?
hsmt
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still there?
krypton
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ok
krypton
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so what will be my final answer?
hsmt
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it is above
krypton
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can u help me with one other questionÉ
hsmt
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if i can, i would be happy to
krypton
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find \[find d/dx (\sqrt{1-x ^{2}}+1/2\cos ^{-1}(x) and verify whether or \not this is equal \to (2x+1)d/dx \sin ^{-1}(-x)\]
hsmt
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ok. any ideas where to start?
hsmt
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oh... and i didnt get anything beyond the arrow... sorry... but i think i have enough to figure it out. :)
krypton
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hmm i dont have an idea
hsmt
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ok, well, it is a rather large function, but it is a quotient (hint). So where might we start with this lovely little thing?
krypton
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hmm..no idea lol
krypton
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dont know anytin about the topic yet
hsmt
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it is ok... remember the quotient rule d(f/g)/dx=[(fprime)g-(gprime)f]/g^2?
hsmt
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in this case the numerator is f=sqrt(1-x^2) +1 and g=2cos-1(x)
hsmt
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do you know the product rule?
krypton
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yes
hsmt
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phew...!! i am so glad. i thought for a sec we were outta options. lol
hsmt
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ok
hsmt
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look at f(x)=sqrt(1-x^2)+1 and g(x)=(2cos-1(x))^-1. does this make sense?
krypton
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hahaha i can still
remember my calculus 1, this calculus 2
krypton
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yes it does
hsmt
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glad to hear it... calc I is totally needed here... good, it makes sense. now we need fprime and gprime and i think you are pretty much homefree. so what is fprime and what is gprime?
hsmt
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just algebra after you get the derivatives.
krypton
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so i should get the derivative of each of them separatelyÉ