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Math Help - Help Needed !! Exponential Differentiation

  1. #1
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    Help Needed !! Exponential Differentiation

    Hi,

    Can anybody help me. How to differentiate this one step by step? Thanks a lot for your kindness.


    F(t) = 0.001/(0.001t + 1)^2 dt
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by zadjrgt View Post
    Hi,

    Can anybody help me. How to differentiate this one step by step? Thanks a lot for your kindness.


    F(t) = 0.001/(0.001t + 1)^2 dt
    Hard way:

    Use the quotient rule: \frac d{d(x)} \frac uv = \frac {u'v - uv'}{v^2}

    here, u = 0.001 and v = (0.001t + 1)^2


    Easy way:

    write as F(t) = 0.001(0.001t + 1)^{-2} and use the chain rule

    chain rule: \frac d{dx} f(g(x)) = f'(g(x)) \cdot g'(x)

    thus we get, F'(t) = -2(0.001)(0.001t + 1)^{-3} \cdot 0.001 = -0.000002(0.001t + 1)^{-3} = - \frac {0.000002}{(0.001t + 1)^3}
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    2 more questions

    Here is my questions :

    how to solve it step by step

    1. e^((integrate 0 to t) 0.4 t dt)

    2. [-d(0.001t +1)^-1 / dt] *[ 1/(0.001t +1)^-1]

    Can anybody help me? Thanks
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  4. #4
    Moo
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    Quote Originally Posted by zadjrgt View Post
    Here is my questions :

    how to solve it step by step

    1. e^((integrate 0 to t) 0.4 t dt)
    e^{\int_0^t 0.4 t \ dt}=e^{0.4 \int_0^t x \ dx}=e^{0.4 \left[x^2/2\right]_0^t}

    =e^{0.4*t^2/2}=e^{0.2 \ t^2}



    Or did you want to differentiate this ?
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    Quote Originally Posted by Moo View Post
    e^{\int_0^t 0.4 t \ dt}=e^{0.4 \int_0^t x \ dx}=e^{0.4 \left[x^2/2\right]_0^t}

    =e^{0.4*t^2/2}=e^{0.2 \ t^2}



    Or did you want to differentiate this ?
    i think that was the answer. Do you know how to solve my second question?
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  6. #6
    Senior Member nikhil's Avatar
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    Quote Originally Posted by zadjrgt View Post
    2. [-d(0.001t +1)^-1 / dt] *[ 1/(0.001t +1)^-1]
    differentiate using chain rule
    -[-1((0.001t +1)^-2)d(0.001t +1)/dt *[ 1/(0.001t +1)^-1]
    =((0.001t +1)^-2))0.001*[ 1/(0.001t +1)^-1]
    =.001/(0.001t +1)
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