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Math Help - derivitive help

  1. #1
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    derivitive help

    Having issue with e^x problems. example:

    ye^x - xe^y = xy find (a) dy/dx and (b) d^2y/dx^2

    I'd likely not have issue with the second derivitive if I could figure the first.

    the xy is easy, just product rule. the other side, however, I'm not sure how to get dy/dx. Is it simply dy/dx ye^x - d/dx xe^y and then you can just use the product rule? If someone can work that out, I can figure out what you did.

    also:

    y=3e^(x^(2-1))*x^(x-1) find y'. I can even begin to describe where I get lost there.

    and:

    lim x->0 (e^-x-1)/(1-e^x)

    I can do these with non e^x but these are the only ones that are throwing me off. Thanks for any help!
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Detroit, MI
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    Quote Originally Posted by BooGTS View Post
    Having issue with e^x problems. example:

    ye^x - xe^y = xy find (a) dy/dx and (b) d^2y/dx^2

    I'd likely not have issue with the second derivitive if I could figure the first.

    the xy is easy, just product rule. the other side, however, I'm not sure how to get dy/dx. Is it simply dy/dx ye^x - d/dx xe^y and then you can just use the product rule? If someone can work that out, I can figure out what you did.

    also:

    y=3e^(x^(2-1))*x^(x-1) find y'. I can even begin to describe where I get lost there.

    and:

    lim x->0 (e^-x-1)/(1-e^x)

    I can do these with non e^x but these are the only ones that are throwing me off. Thanks for any help!
    The dirivative of e^x is e^x !

    When differentiating with respect to x, \frac{d}{dx}e^y=e^y\frac{dy}{dx}

    It's that easy!

    So your problem ye^x-xe^y=xy

    You've gotta use the power rule in each term so that

    (ye^x+e^x\frac{dy}{dx})-(xe^y\frac{dy}{dx}+e^y)=(x\frac{dy}{dx}+y)
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  3. #3
    MHF Contributor Amer's Avatar
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    Jordan
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    Quote Originally Posted by BooGTS View Post
    Having issue with e^x problems. example:

    ye^x - xe^y = xy find (a) dy/dx and (b) d^2y/dx^2

    I'd likely not have issue with the second derivitive if I could figure the first.

    the xy is easy, just product rule. the other side, however, I'm not sure how to get dy/dx. Is it simply dy/dx ye^x - d/dx xe^y and then you can just use the product rule? If someone can work that out, I can figure out what you did.

    also:

    y=3e^(x^(2-1))*x^(x-1) find y'. I can even begin to describe where I get lost there.

    and:

    lim x->0 (e^-x-1)/(1-e^x)

    I can do these with non e^x but these are the only ones that are throwing me off. Thanks for any help!

    lim_{x\rightarrow 0} \frac{e^{-x}-1}{1-e^x}

    lim_{x\rightarrow 0 } \frac{\frac{1}{e^x} - 1 }{1-e^x }

    make the denominator in the numerator the same ( I do not know what you called this operation ) after you do that it will be easy
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  4. #4
    MHF Contributor Amer's Avatar
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    Jordan
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    Quote Originally Posted by BooGTS View Post
    y=3e^(x^(2-1))*x^(x-1) find y'. I can even begin to describe where I get lost there.
    I will solve an example similar to your question

    y=4e^{x^2}(x^{\sin x})

    y'=4\left(\frac{d}{dx}e^{x^2}\right)(x^{\sin x})+4\left(\frac{d}{dx}(x^{\sin x})\right)(e^{x^2})

    y'=4(2xe^{x^2})(x^{\sin x})+4(\cos x)(ln(x)(x^{\sin x })(e^{x^2})

    y'=(8xe^{x^2})(x^{\sin x})+4\ln (x)(\cos x)(x^{\sin x })(e^{x^2})

    note that

    \frac{d}{dx} x^{f(x)} = f'(x) ln(x)x^{f(x)} f(x) is a function

    \frac{d}{dx} e^{f(x)} = f'(x) e^{f(x)}
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