maths question

I thought this was interesting too.  I'd like to make it both simpler (1. below) and more complicated (2. below)!

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$\mbox{what do you know about the relationship between }f^\prime(x) \mbox{ and }(f^{-1})^\prime(x) ?$

Rom, I hope that you do not mind me butting in but i could not answer your questions straight off and I wanted to think about what was happening myself.

So whether or not you are teaching the question asker, you are teaching me:)

I developed a formula for a curve that met the given criterion.

This is what I came up with.  

https://www.desmos.com/calculator/7uhpqmscci

I/You did not need to do any of this to answer the question, I was just thinking laterally. :)

The answer is very simple.

Thanks Alan,

In response to 1).

Yes of course I could have         LOL

BUT

The graph would not hve looked as interesting   

In response to 2)

That makes my head hurt.    

Maybe I will think about it later after something deadens the pain.             LOL   again    

1. You are right Melody, the graph would have been really boring!  

2. Here are a couple of graphs to illustrate the solution when n = 2 (so f(x) = x⁵ + 7) 

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Thanks Alan,  I still like my graph.             

I need to look at your number 2 answer properly :))

all very nice work but you all seemed to have missed the point

$\left(f^{-1}\right)^\prime(x)=\dfrac 1 {f^\prime(f^{-1}(x))}$

$\mbox{So as }f \mbox{ has a tangent line }y=5x+3, @(1,8) \\ {f^{-1}}^\prime(8) = \dfrac 1 {f^\prime(1)}=\dfrac 1 {5(1)+3}=\dfrac 1 8$