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Bio
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Longest streak: 115 days
212 thank you notes
Bio
Bio joined Socratic
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karma
· Singapore
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Activity
750 Answers
366 Edits
1 Asked
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@bio Bio updated the answer to Why are convex mirrors used instead of concave mirrors as rear view mirrors? .
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@bio Bio updated the answer to Which gas turns lime to water milky? (Oxygen/Carbon dioxide) .
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@bio Bio wrote an answer to How do you solve #abs(8-2n)=2#? .
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@bio Bio wrote an answer to How do you find the average value of the function for #f(x)=2-1/2x, 0<=x<=4#? .
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@bio Bio commented @Slithern You are right on How do you solve #2sin^2x-cosx=1# on the interval [0,2pi]?
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@bio Bio wrote an answer to How do you find the points of intersection of #theta=pi/4, r=2#? .
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@bio Bio commented If the inverse of #f'(x)# exists, then you will get
#x = f^(-1)(y)#
or
#y = f(x)# on Can someone explain why this happens? -
@bio Bio commented Therefore, the Above Equation simplifies to
#f'(x) = 1/{d/{dy}(f^(-1)(y))} = f'(f^(-1)(y))#
or to write it more clearly
#f'(x) = f'(f^(-1)(y))# on Can someone explain why this happens? -
@bio Bio commented However, as mentioned by Jim, the right side can be simplified. In particular,
#d/{dy}(f^(-1)(y))#
#= d/{dy}(x)#
#= 1/({dy}/{dx})#
#= 1 / ( f'(x) )#
#= 1 / ( f'( f^(-1)(y) ) )# on Can someone explain why this happens? -
@bio Bio commented The reason is because for the Above Equation to hold, #y=f(x)# is a pre-requisite, In other words,
#y = f(x) implies f'(x) = 1/{d/{dy}(f^(-1)(y))}#
but not the other way round. on Can someone explain why this happens? - Show more activity
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