The discussion focuses on computing the derivative of the function (sin(x))^2 using the product rule and quotient rule, explicitly avoiding the chain rule. The derivative is calculated as 2(sin(x))(cos(x)), which is confirmed to be equivalent to sin(2x) based on trigonometric identities. Participants agree on the correctness of the solution and its simplification.
PREREQUISITESStudents studying calculus, particularly those focusing on differentiation techniques, and educators seeking to reinforce concepts related to the product and quotient rules.
Looks fine to me. The final answer is equivalent to sin(2x) [trig identity] in case you want a slightly simpler form.Torshi said:Homework Statement
compute the following derivatives using the product rule and quotient rule as necessary, without using chain rule.
Homework Equations
d/dx ((sin(x))^2)
The Attempt at a Solution
=(sin(x))(sin(x))
=(cos(x))(sin(x))+(sin(x))(cos(x))
=2(sin(x))(cos(x))
jbunniii said:Looks fine to me. The final answer is equivalent to sin(2x) [trig identity] in case you want a slightly simpler form.