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Math - Derivatives

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How would one take the derivative of "f(x)^[g(x)]? Is there a formula I can follow to differentiate functions like that?

  • Math - Derivatives - ,

    you will have to take the natural log of both sides.
    I will illustrate with an example

    e.g.

    y = (x^2+1)^(2x+3)
    ln y = ln ((x^2+1)^(2x+3))
    ln y = (2x+3)(ln(x^2+1)

    now differentiate, using the product rule on the right side.
    (dy/dx)/y = (2x+3)(2x/(x^2+1)) + 2ln(x^2+1)
    dy/dx = y((2x+3)(2x/(x^2+1)) + 2ln(x^2+1))
    you could then replace y with its original value and simplify, but that would be a general method.

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