The discussion focuses on finding the equation of the tangent line to the curve defined by the function y = ln(xe^(x²)) at the point P=(1, 1). The key steps involve applying logarithmic properties to simplify the function into y = ln(x) + ln(e^(x²)), which further simplifies to y = ln(x) + x². The derivative is then calculated using the chain rule and the properties of logarithmic differentiation, leading to the slope needed for the Point-Slope formula.
PREREQUISITESStudents studying calculus, particularly those focusing on differentiation and tangent line equations, as well as educators seeking to reinforce these concepts in a classroom setting.
First, use the properties of logarithms; namely ln(a*b) = ln a + ln b. Then, take the derivative. Presumably you know how to differentiate y = ln u, where u is a function of x.b521 said:Homework Statement
Find an equation of the tangent line to the curve at the
given point.
y = ln(xe^(x²)) P=(1, 1)
The Attempt at a Solution
I know how to plug in the numbers into the Point-Slope formula once I find the derivative of the function, or slope, I'm just not sure how to derive this function.