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Bio has helped students
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Longest streak: 115 days
212 thank you notes
Someone from United States
really helped me figure out this as im going into exams and my teacher was unable to simply explain.
for this
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yesterday
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Someone from Saint Charles, United States
that was very helpful
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yesterday
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Someone from San Francisco, United States
Cool
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1 week ago
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Bio
Bio joined Socratic 2 years ago. Bio hasn't written a biography yet.
189K karma · Singapore
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Activity
750 Answers
366 Edits
1 Asked
@bio
Bio
updated
the answer to
Why are convex mirrors used instead of concave mirrors as rear view mirrors?
.
2 weeks ago
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@bio
Bio
updated
the answer to
Which gas turns lime to water milky? (Oxygen/Carbon dioxide)
.
1 month ago
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Nicki liked this.
@bio
Bio
wrote an answer to
How do you solve #abs(8-2n)=2#?
.
1 month ago
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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#?
.
1 month ago
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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]?
1 month ago
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@bio
Bio
wrote an answer to
How do you find the points of intersection of #theta=pi/4, r=2#?
.
2 months ago
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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?
2 months ago
·
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@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?
2 months ago
·
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@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?
2 months ago
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@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?
2 months ago
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