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