-1 ------ cos(x) e
/ -1 \ | ------| d | cos(x)| --\e / dx
Let .
The derivative of is itself.
Then, apply the chain rule. Multiply by :
The derivative of a constant times a function is the constant times the derivative of the function.
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:
So, the result is:
The result of the chain rule is:
The answer is:
-1 ------ cos(x) -e *sin(x) ---------------- 2 cos (x)
-1 / 2 2 \ ------ | sin (x) 2*sin (x)| cos(x) |-1 + ------- - ---------|*e | 3 2 | \ cos (x) cos (x) / ---------------------------------- cos(x)
-1 / 2 2 2 \ ------ | 3 sin (x) 6*sin (x) 6*sin (x)| cos(x) |-5 + ------ - ------- - --------- + ---------|*e *sin(x) | cos(x) 4 2 3 | \ cos (x) cos (x) cos (x) / -------------------------------------------------------------- 2 cos (x)