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Alex
Alex asked in Science & MathematicsMathematics · 1 decade ago

If the derivative of e^x is equal to e^x, why is the derivative of e^x^2 not e^x^2 (why is chain rule used)?

Thanks :)

4 Answers

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  • Todd
    Lv 6
    1 decade ago
    Favorite Answer

    Technically, the chain rule is used on both of them.

    d/dx e^x = e^x * d/dx (x) = e^x * 1 = e^x.

    d/dx e^(x^2) = e^(x^2) * d/dx (x^2) = e^(x^2) * 2x.

  • Anonymous
    1 decade ago

    Because the outside equation is x^2 and the inside is e^x. Always remember "derivative of the outside leaving the inside alone multiplied by the derivative of the inside. So the derivative of e^x^2 is 2(e^x)(e^x)

  • alangoestomusicwood
    Lv 5
    1 decade ago

    because

    d/dx e^x = e^x * (x)' = e^x

    whereas

    d/dx e^x^2 = e^x^2 * (x^2)' = 2x*e^x^2

  • harry m
    Lv 6
    1 decade ago

    (why is chain rule used) = it's always used

    y = e^x

    => dy/dx = e^x * d/dx(x)

    => dy/dx = e^x *1

    y = e^5x

    => dy/dx = e^5x * d/dx(5x)

    => dy/dx = e^5x *5

    y = e^(x^2 )

    => dy/dx = e^(x^2 ) * d/dx(x^2 )

    => dy/dx = e^(x^2 ) *2x

    QED

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