What is the equation of the normal line of #f(x)=sqrt(e^x-x+1)/e^(2x)# at #x = 0#?
The slope of the tangent line is the first derivative evaluated at the the given x coordinate. The slope of the normal line is the negative of the reciprocal of the slope of the tangent line.
Compute the first derivative:
Evaluate at x = 0:
The slope of the normal line is:
Using the slope-intercept form of the equation of a line: