The discussion focuses on finding the derivative dy/dx for the equation r = x^2 tan(2x) by substituting r for y and theta for x. The initial attempt incorrectly applies the product rule and chain rule, leading to an erroneous result of dy/dx = 4x sec^2(2x). The correct approach requires the application of the product rule to differentiate the product of x^2 and tan(2x), ensuring accurate results in calculus.
PREREQUISITESStudents studying calculus, particularly those learning about differentiation techniques, as well as educators looking for examples of product and chain rule applications in real problems.
The line above is wrong. x^2 * tan(2x) is a product, so you need to use the product rule. You are using the chain rule correctly, below.Minihoudini said:Homework Statement
substituting r for y and theta for x as it will be easier to read
find dy/dx if r=x^2 tan(2x)
I don't know the answer
Homework Equations
The Attempt at a Solution
d/dx (y) = d/dx [x^2 tan(2x)]
dy/dx = dx/dx [2x] d/dx [tan (2x)]
Minihoudini said:dy/dx = 2x sec^2 (2x) (2)
dy/dx = 4x sec^2 (2x)
its wrong though