1. ## Normal Line

What is the equation of the line normal to the curve y=(ln(x))* e raised to (2x) where x=1? I just don't know how to find normal lines.

What is the equation of the line normal to the curve y=(ln(x))* e raised to (2x) where x=1? I just don't know how to find normal lines.
know how to find a tangent line?

normal lines are perpendicular to tangent lines.

3. I just drew a blank on how to find tangent lines. Derivative? I know perpendicular means the slope is the negative reciprocal.

4. The normal at the point $\displaystyle \left( {a,f(a)} \right)$ is $\displaystyle y - f(a) = \frac{{ - 1}}{{f'(a)}}\left( {x - a)} \right)$.

I just drew a blank on how to find tangent lines. Derivative? I know perpendicular means the slope is the negative reciprocal.
use the derivative to find the slope at at the given point ... normal slope will be the opposite reciprocal of that slope. finally, use the point-slope form to get the equation.

6. I don't understand.

$\displaystyle y = \ln{x} \cdot e^{2x}$