# Thread: Exponential Functions: Differentiation and Integration

1. ## 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

2. Originally Posted by bilderback
I have no idea how to answer these problems

Solve for x

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

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

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

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

implicit derivative ...

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

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

Solve the differential equation

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

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

finish it
...