The derivative of the function f(x) = sin(sin(sin(x))) is calculated using the chain rule. The correct derivative is df/dx = cos(sin(sin(x))) * cos(sin(x)) * cos(x). This solution confirms the application of the chain rule twice, demonstrating the nested nature of the sine function. Participants in the discussion validated the solution, emphasizing the importance of understanding the chain rule in calculus.
PREREQUISITESStudents studying calculus, mathematics educators, and anyone looking to deepen their understanding of differentiation techniques, particularly with trigonometric functions.
jedishrfu said:yes use the chain rule:
f(x)=sin(sin(x))
df/dx = cos(sin(x)) * cos(x)
your solution looks correct.
Torshi said:Well the original problem was f(x) = (sin(sin(sin(x)))), but yes I believe I got it right. Thank you.
jedishrfu said:I know that but at first I didn't want to give you the answer outright. Later as I reread your post I saw that you had in fact the right answer. Anyway, its helpful to see a simpler example.