3 sin(x)*cos (x)
sin(x)*cos(x)^3
Apply the product rule:
; to find :
The derivative of sine is cosine:
; to find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of cosine is negative sine:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
4 2 2 cos (x) - 3*cos (x)*sin (x)
/ 2 2 \ \- 10*cos (x) + 6*sin (x)/*cos(x)*sin(x)
4 2 / 2 2 \ 2 2 2 / 2 2 \ - cos (x) - 3*sin (x)*\- 7*cos (x) + 2*sin (x)/ + 9*cos (x)*sin (x) + 9*cos (x)*\- cos (x) + 2*sin (x)/