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    What's so special about y=e^x???

    I cant remember but my teacher said something about the gradient equalling the same y value n the y axis or something... o.o
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    (Original post by bigdonger)
    What's so special about y=e^x???

    I cant remember but my teacher said something about the gradient equalling the same y value n the y axis or something... o.o
    Do ln of both sides you get lny = x
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    Differentiate or integrate y with respect to x and you get e^x again.
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    (Original post by bigdonger)
    What's so special about y=e^x???

    I cant remember but my teacher said something about the gradient equalling the same y value n the y axis or something... o.o
    The gradient of y = e^x is equal to e^x.
    When you differentiate y = e^x you get dy/dx = e^x... This is not true for y = e^2x (or any other function of x), however. You will learn this once you cover the differentiation chapter in C3
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    (Original post by Reda2)
    Do ln of both sides you get lny = x
    ok... so what does that mean? ...
    oh i see ok but is that's all that's special about y=e^x?
    (Original post by Wunderbarr)
    Differentiate or integrate y with respect to x and you get e^x again.
    yup teacher told me that
    (Original post by JLegion)
    The gradient of y = e^x is equal to e^x.
    When you differentiate y = e^x you get dy/dx = e^x... This is not true for y = e^2x, however. You will learn this once you cover the differentiation chapter in C3
    oh? is there proof for this? how does one know?
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    (Original post by bigdonger)
    oh? is there proof for this? how does one know?
    You will learn this in the C3 differentiation chapter.

    I believe the proof for this is beyond the A-Level syllabus
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    (Original post by bigdonger)
    ok... so what does that mean? ...
    oh i see ok but is that's all that's special about y=e^x?

    yup teacher told me that

    oh? is there proof for this? how does one know?
    y = e^x
    lny = lne^x
    lny = x
    (Implicit diff wrt x)
    (1/y)(dy/dx) = 1
    dy/dx = y
    dy/dx = e^x

    combine that with: https://www.khanacademy.org/math/dif...-d-dx-ln-x-1-x
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    (Original post by JLegion)
    You will learn this in the C3 differentiation chapter.

    I believe the proof for this is beyond the A-Level syllabus
    ah ok
    (Original post by XOR_)
    y = e^x
    lny = lne^x
    lny = x
    (Implicit diff wrt x)
    (1/y)(dy/dx) = 1
    dy/dx = y
    dy/dx = e^x

    combine that with: https://www.khanacademy.org/math/dif...-d-dx-ln-x-1-x
    probably need to earn that bit, i understand the rest though.....
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    e is a special number because it is the base of the natural logarithm. It is a special number and comes up a lot in growth and decay. It is defined in many ways but I think the most natural way is that it can be defined as
     \displaystyle e= \lim_{n\to\infty } \left (1+\frac{1}{n} \right )^n .
 
 
 
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