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Differntiating inverse trigonometric functions

Chuchoter · 2012-05-06 16:58:17

I can do these when its a constant on the bottom as I can find examples of sin^-1 (x/a), but how do you do the ones where its got an x on the bottom? Like tan^-1(2x/x+5) for example? I've seen ones where you multiply by the differentiate but they seem very messy.

06-05-2012 5:58pm

#1

Chuchoter

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I can do these when its a constant on the bottom as I can find examples of sin^-1 (x/a), but how do you do the ones where its got an x on the bottom? Like tan^-1(2x/x+5) for example? I've seen ones where you multiply by the differentiate but they seem very messy.

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#2 06-05-2012 6:18pm

finality

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Think of it as (2x/x+5)/1

2x/x + 5 is x in the tables
and 1 is a

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#3 06-05-2012 6:21pm

Chuchoter

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Thank you!

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#4 06-05-2012 7:25pm

MathsManiac

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Don't forget that you'll also need to multiply by the derivative of what's in thebrackets, (as it's a chain rule).

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#5 06-05-2012 8:32pm

unmoeglichkeit

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You could always differentiate implicitly, just change the function to

y= tan^-1(2x/x+5)
tany=2x/x+5

and then use implicit differentiation

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