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Math Help - Exponential Functions: Differentiation and Integration

  1. #1
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    Exponential Functions: Differentiation and Integration

    I have no idea how to answer these problems

    Solve for x

    ln((x-4)^2)=14

    Find an equation of the tangent line to the graph of the function at the point (1, 1).

    1+ln(xy)=e^x

    Solve the differential equation

    dy/dx=(9e^x-2e^-x)^2
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  2. #2
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    Quote Originally Posted by bilderback View Post
    I have no idea how to answer these problems

    Solve for x

    ln((x-4)^2)=14

    \textcolor{red}{(x-4)^2 = e^{14}}

    solve for x

    Find an equation of the tangent line to the graph of the function at the point (1, 1).

    1+ln(xy)=e^x

    \textcolor{red}{1 + \ln{x} + \ln{y} = e^x}

    implicit derivative ...

    \textcolor{red}{\frac{1}{x} + \frac{1}{y} \cdot \frac{dy}{dx} = e^x}

    determine the slope at the indicated coordinates, then write the tangent line equation.

    Solve the differential equation

    dy/dx=(9e^x-2e^-x)^2

    \textcolor{red}{y = \int 81e^{2x} - 36 + 4e^{-2x} \, dx}

    finish it
    ...
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