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Math - Derivatives

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I find it difficult to take the derivative of something that has a constant base with a variable as an exponent...and simplify it... PLEASE HELP ME!

f(x) = e^(x^(-1))

f'(x) = -1(e^(x^(-2))e^(x^(-1))

f'(x) = -e^(x^(-2))e^(x^(-1))

?????

and... f(x) = 3^x

f'(x) = 3^x

  • Math - Derivatives -

    d/dx e^u = e^u du/dx
    here u = x^-1
    du/dx = -1 x^-2
    so
    d/dx e^(x^-1) = -x^-2 e^(x^-1)
    = -(1/x^2)e^(1/x^2)
    Try the others using that recipe:
    d/dx e^u = e^u du/dx

  • Math - Derivatives -

    WOW that actually helps a lot and less confusing to solve! Thanks so much!

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