The discussion focuses on deriving the function y = (cos{x}sin{2x})^{-2} using the power rule and product rule in calculus. The incorrect initial attempt led to a misunderstanding of the derivative, resulting in a different answer than the correct one, which is 4(3sin{2x} - 1) / (cos{2x}sin^{3}{2x}). The correct approach involves applying the product rule to find the derivative of cos{x}sin{2x} before applying the power rule.
PREREQUISITESStudents studying calculus, particularly those focusing on derivatives involving trigonometric functions, and educators seeking to clarify the application of differentiation rules.
cinematic said:Homework Statement
Derive the following:
y = (cosxsin2x)-22. The attempt at a solution
Basically I saw this as a power rule with two products in the middle.
So y = -2 (cos2cos2x-sinxsin2x)-1
But the correct answer is completely different, it's:
4(3sin2x - 1) all over
cos2xsin32x
Could someone please go through the steps to get to the correct solution? Thanks in advance!