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Math Help - Difficult differentiation of e questions.

  1. #1
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    Difficult differentiation of e questions.

    differentiate the following
    y= e^(4x+1)*(x+1)^2

    y= e^(-4x)square root (x+1), x>-1

    y= X^4 e^-2x

    y= (1/x)e^x

    (x^2 + 2x + 2)e^-x



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  2. #2
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    catch words: chain and product rule

    good luck
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  3. #3
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    i can do the basic ones, i just can't do these ones in particular
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by chaneliman View Post
    differentiate the following
    y= e^(4x+1)*(x+1)^2 Use product and chain rules: \color{red}\boxed{\frac{dy}{dx}=4e^{4x+1}(x+1)^2+2  e^{4x+1}(x+1)}

    y= e^(-4x)square root (x+1), x>-1 Again, use product and chain rules: \frac{dy}{dx}=-4e^{-4x}\sqrt{x+1}+\frac{e^{-4x}}{2\sqrt{x+1}}=\color{red}\boxed{-\frac{(4x+3)e^{-4x}}{\sqrt{x+1}}}

    y= X^4 e^-2x Again, use product and chain rules: \color{red}\boxed{\frac{dy}{dx}=4x^3e^{-2x}-2x^4e^{-2x}}

    y= (1/x)e^x Apply quotient rule: \frac{dy}{dx}=\frac{xe^x-e^x}{e^{2x}}=\color{red}\boxed{\frac{x-1}{e^x}}

    (x^2 + 2x + 2)e^-x Use product and chain rules: \frac{dy}{dx}=(2x+2)e^{-x}-(x^2+2x+2)e^{-x}=\color{red}\boxed{-x^2e^{-x}}



    Thanks
    Does this make sense?

    --Chris
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