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    Hi, Can someone please explain the 3rd line? Name:  math.jpg
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    (Original post by Banana ice-cream)
    Hi, Can someone please explain the 3rd line? Name:  math.jpg
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    What don't you understand? Differentiating \ln y with respect to x gets you \frac{1}{y} \frac{dy}{dx} and differentiating x\ln a with respect to x gets you \ln a.

    So all they've done is differentiated both sides of the second line.
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    (Original post by Zacken)
    What don't you understand? Differentiating \ln y with respect to x gets you \frac{1}{y} \frac{dy}{dx} and differentiating x\ln a with respect to x gets you \ln a.

    So all they've done is differentiated both sides of the second line.
    When you differenciate x ln a with respect to x, why don't you get 1/a?
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    (Original post by Banana ice-cream)
    When you differenciate x ln a with respect to x, why don't you get 1/a?
    Because a is just a number, and so is \ln a. You wouldn't say that if you differentiate x\ln 2 you'd get \frac{1}{2}, would you?

    So, since \ln a is a constant then \frac{d}{dx}(x \ln a) = \ln a \frac{d}{dx}(x) = \ln a.
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    (Original post by Zacken)
    Because a is just a number, and so is \ln a. You wouldn't say that if you differentiate x\ln 2 you'd get \frac{1}{2}, would you?

    So, since \ln a is a constant then \frac{d}{dx}(x \ln a) = \ln a \frac{d}{dx}(x) = \ln a.
    I still don't understand. But then, when you differentiate y=lnx why do you get dy/dx = 1/x?
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    (Original post by Banana ice-cream)
    I still don't understand. But then, when you differentiate y=lnx why do you get dy/dx = 1/x?
    Because x isn't a constant, it is the variable you are differentiating with respect to. If you did \frac{d}{da} \ln a then you'd get \frac{1}{a}. But here you are doing \frac{d}{dx} (x\lna) = \ln a.
 
 
 
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