/ 2 \ cos\log (x) + 3/
d / / 2 \\ --\cos\log (x) + 3// dx
Let .
The derivative of cosine is negative sine:
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of is .
The result of the chain rule is:
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
Now simplify:
The answer is:
/ 2 \ -2*log(x)*sin\log (x) + 3/ -------------------------- x
/ / 2 \ / 2 \ 2 / 2 \\ 2*\- sin\3 + log (x)/ + log(x)*sin\3 + log (x)/ - 2*log (x)*cos\3 + log (x)// ----------------------------------------------------------------------------- 2 x
/ / 2 \ / 2 \ / 2 \ 3 / 2 \ 2 / 2 \\ 2*\3*sin\3 + log (x)/ - 6*cos\3 + log (x)/*log(x) - 2*log(x)*sin\3 + log (x)/ + 4*log (x)*sin\3 + log (x)/ + 6*log (x)*cos\3 + log (x)// ---------------------------------------------------------------------------------------------------------------------------------------- 3 x