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Differential Calculus

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14 Mar 2010 16:21:18 IST

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Is it possible to differentiate exp and log functions where bases are functions not constants?How?

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Is it possible to differentiate exp and log functions where bases are functions not constants?How?

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never say never

Hot goIITian

Joined: 19 Nov 2009

Posts: 153

15 Mar 2010 06:45:20 IST

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yes apply base change formula

y=log base cos sinx=logsinx/log cosx =log(sinx- cosx)

e^y =sinx-cosx

differentiate

ye^ydy/dx=cosx+sinx

dy/dx=cos+sinx/ye^y

HIMANSHU JAIN

Scorching goIITian

Joined: 8 Feb 2007

Posts: 267

15 Mar 2010 16:43:31 IST

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@sdfgh: logm/logn is not equal to logm - logn

log (m/n) =log m - log n.

yes, differentiation is possible, logm with base n can be written as logm/logn.

Now, you can easily differentiate it by division rule.

If still any problem, feel free to ask.

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