Math Is Fun Forum

EMPhillips1989

Member

Registered: 2008-01-21

Posts: 40

differentiation

hi
i was wondering how i would differentiate an exponetial of the form:

if im differentiating with respect to x does the equation stay the same or become:

as there's both x and y variables im slightly confused??? please help!!

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: differentiation

you can only differentiate it like that by having y as a constant.

infact in multi-variable calculus as far as i know (i have only self-studied very little) you can only take partial derivitives, that is imagine that one of the variables is constant and differentiate which taking the two partial derivitives gives the gradient vector for the surface at that point (x,y)

i.e.

basicly, imagine if you plot a 3d graph of z = e^{xy}. then if you trace a line down the surface where 'x' is constant. and imagine that as a 2d graph, the gradient is the partial derivitive in y. and if you trace a line down the surface where 'y' is constant, and imagine that as a 2d graph, the gradient is the partial derivitive in x

Last edited by luca-deltodesco (2008-01-24 05:30:35)

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JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: differentiation

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: differentiation

supposing he has a differentiable function for y in x, but still i wouldn't have thought to do it like that, thanks

Last edited by luca-deltodesco (2008-01-24 05:44:29)

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The Beginning Of All Things To End.
The End Of All Things To Come.