help with a question please, cheers ;) Watch

Toneh
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OK in a random c3 maths thread i saw on the homepage there was the question someone posted to differentiate 7e^{x^y}

this is what I did, but I'd like someone a bit more qualified to tell me if it's right or not

Derivative of e^{f(x)} = f'(x)e^{f(x)}
therefore if we can find the derivative of x^y, we can do the rest pretty easily.
So, x^y is a bit tricky, but as far as I can see, x^y = e^{ylnx}
therefore we can differentiate e^{ylnx} using the rule above and the product rule:
(lnx(\frac{dy}{dx}) + (\frac{y}{x}))e^{ylnx}

Therefore;
(7(lnx(\frac{dy}{dx}) + (\frac{y}{x}))e^{ylnx})e^{x^y} = \frac{d}{dx}(7e^{x^y})

I think

:P
Last edited by Toneh; 8 years ago
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Notnek
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Almost.

e^{y \ln x} has disappeared in the final equation.

This all assumes that y depends on x and is not just a constant (and you're differentiating wrt x).
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Toneh
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(Original post by notnek)
Almost.

e^{y \ln x} has disappeared in the final equation.

This all assumes that y depends on x and is not just a constant (and you're differentiating wrt x).
is that right then? (the edit)
and yer I know it's assuming that, but that;'s the whole point - it's boring otherwise.
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victor_b1992
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i got 7Y^y-1xe^x^y
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Toneh
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(Original post by victor_b1992)
i got 7Y^y-1xe^x^y
how did you work it out...cos that's different to mine, but unless you post your workings we can't really compare :P
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Notnek
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THe original post is now correct.
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victor_b1992
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(Original post by Toneh)
how did you work it out...cos that's different to mine, but unless you post your workings we can't really compare :P
i use the chain rule iam pretty show this is correct.

as differentiation of x^y= yx^y-1
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Toneh
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(Original post by victor_b1992)
i use the chain rule iam pretty show this is correct.

as differentiation of x^y= yx^y-1
well yes that works if y is a constant, but i was differentiating it where y was a variable, so that doesn't work.
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victor_b1992
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(Original post by Toneh)
well yes that works if y is a constant, but i was differentiating it where y was a variable, so that doesn't work.
so what did you get
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Toneh
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(Original post by victor_b1992)
so what did you get
it's in the OP...
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victor_b1992
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ok i see what you did kl sorry my head is just not screwed on property today.
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