- #1
Robokapp
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I'm guessing not a lot will care about this becasue it's not very relevant, but my calc teacher couldn't do this and I did it in a few seconds, so i'll expose it.
The problem stated that f(x)=x^3+x
and inverse of f(x)=g(x) and g(2)=1
question: Find g'(2)
----------------------------
My teacher tried to create a formula to connect inverse derivative answers and inverse functions for cubics. He couldn't. So while staring at it I realize how the derivative is dy/dx which is appearing everywhere you derivate a y.
so I write y=x^3+x
take inverse x=Y^3+y
and I don't care about what the function looks like. I don't worry about putting it in standard form like he tried. I keep it like this and take derivative. Out of nowhere I might say I had written down 1=3y^2 dy/dx + dy/dx
and isolating the dy/dx => dy/dx = 1/(1+2y^2)
since point (2,1) was given, the fact that I have no x is not important. i can plug in y instead. And I get the final answer. g'(2)=1/4
The relevance of this is that finding the derivative of a function can be expressed in many forms, related to various letters in that expression. many times the y' has both x and y.
But...Standard form was not important here, and pretty much everyone, myslef included for a few minutes were hooked up on putting it in standard form...
I thought i'd share this with you.
~Robokapp
The problem stated that f(x)=x^3+x
and inverse of f(x)=g(x) and g(2)=1
question: Find g'(2)
----------------------------
My teacher tried to create a formula to connect inverse derivative answers and inverse functions for cubics. He couldn't. So while staring at it I realize how the derivative is dy/dx which is appearing everywhere you derivate a y.
so I write y=x^3+x
take inverse x=Y^3+y
and I don't care about what the function looks like. I don't worry about putting it in standard form like he tried. I keep it like this and take derivative. Out of nowhere I might say I had written down 1=3y^2 dy/dx + dy/dx
and isolating the dy/dx => dy/dx = 1/(1+2y^2)
since point (2,1) was given, the fact that I have no x is not important. i can plug in y instead. And I get the final answer. g'(2)=1/4
The relevance of this is that finding the derivative of a function can be expressed in many forms, related to various letters in that expression. many times the y' has both x and y.
But...Standard form was not important here, and pretty much everyone, myslef included for a few minutes were hooked up on putting it in standard form...
I thought i'd share this with you.
~Robokapp