sin(x) ------- 2 cos (x)
sin(x)/cos(x)^2
Apply the quotient rule, which is:
and .
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:
Now plug in to the quotient rule:
Now simplify:
The answer is:
2 cos(x) 2*sin (x) ------- + --------- 2 3 cos (x) cos (x)
/ 2 \ | 6*sin (x)| |5 + ---------|*sin(x) | 2 | \ cos (x) / ---------------------- 2 cos (x)
/ 2 \ 2 | 3*sin (x)| 8*sin (x)*|2 + ---------| 2 | 2 | 12*sin (x) \ cos (x) / 5 + ---------- + ------------------------- 2 2 cos (x) cos (x) ------------------------------------------ cos(x)