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Math Help - Simplifying equation in to stages to follow...

  1. #1
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    Simplifying equation in to stages to follow...

    Hi Guys,

    I'm a little stuck on how on to differentiate when equations involve e and ln. How would I go about differentiating y= e^x^2 ln x for instance ?

    Thanks for your help.
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  2. #2
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    Re: Simplifying equation in to stages to follow...

    Quote Originally Posted by Cyclo View Post
    Hi Guys,

    I'm a little stuck on how on to differentiate when equations involve e and ln. How would I go about differentiating y= e^x^2 ln x for instance ?

    Thanks for your help.
    Please use parantheses for grouping!

    Which one of the following equations do you mean:

    y= e^(x^2)*ln (x) ---- > \displaystyle{y = e^{x^2} \cdot \ln(x)}

    y= e^((x^2)* ln (x)) ---- > \displaystyle{y = e^{x^2 \cdot \ln(x)}}

    y= e^(x^(2* ln (x))) ---- > \displaystyle{y = e^{x^{(2 \cdot \ln(x))}}
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  3. #3
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    Re: Simplifying equation in to stages to follow...

    Quote Originally Posted by earboth View Post
    Please use parantheses for grouping!

    Which one of the following equations do you mean:

    y= e^(x^2)*ln (x) ---- > \displaystyle{y = e^{x^2} \cdot \ln(x)}

    y= e^((x^2)* ln (x)) ---- > \displaystyle{y = e^{x^2 \cdot \ln(x)}}

    y= e^(x^(2* ln (x))) ---- > \displaystyle{y = e^{x^{(2 \cdot \ln(x))}}
    Apologies. I mean the first one.
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  4. #4
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    Re: Simplifying equation in to stages to follow...

    Quote Originally Posted by Cyclo View Post
    Apologies. I mean the first one.
    y = e^{x^2}\cdot\ln x

    Use the product rule:

    \frac{dy}{dx} = e^{x^2}\cdot\frac d{dx}\left[\ln x\right] + \ln x\cdot\frac d{dx}\left[e^{x^2}\right]

    Can you finish?
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  5. #5
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    Re: Simplifying equation in to stages to follow...

    Quote Originally Posted by Reckoner View Post
    y = e^{x^2}\cdot\ln x

    Use the product rule:

    \frac{dy}{dx} = e^{x^2}\cdot\frac d{dx}\left[\ln x\right] + \ln x\cdot\frac d{dx}\left[e^{x^2}\right]

    Can you finish?
    I'm not sure I have the full understanding of the terms, but here goes...

    I'll have to read up on how to use the correct math text.

    2x*e^xsquared*1/x
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  6. #6
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    Re: Simplifying equation in to stages to follow...

    Quote Originally Posted by Cyclo View Post
    I'm not sure I have the full understanding of the terms, but here goes...

    I'll have to read up on how to use the correct math text.

    2x*e^xsquared*1/x
    You can't just take the derivative of one factor and multiply it by the derivative of the other factor. As I said, we have to use this product rule:

    \frac d{dx}[uv] = u\frac{dv}{dx} + v\frac{du}{dx}.

    So your answer, before simplification, should have two terms.
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