cos(x) ------ log(x)
cos(x)/log(x)
Apply the quotient rule, which is:
and .
To find :
The derivative of cosine is negative sine:
To find :
The derivative of is .
Now plug in to the quotient rule:
Now simplify:
The answer is:
sin(x) cos(x) - ------ - --------- log(x) 2 x*log (x)
/ 2 \ |1 + ------|*cos(x) 2*sin(x) \ log(x)/ -cos(x) + -------- + ------------------- x*log(x) 2 x *log(x) ---------------------------------------- log(x)
/ 3 3 \ / 2 \ 2*|1 + ------ + -------|*cos(x) 3*|1 + ------|*sin(x) | log(x) 2 | 3*cos(x) \ log(x)/ \ log (x)/ -------- - --------------------- - ------------------------------- + sin(x) x*log(x) 2 3 x *log(x) x *log(x) --------------------------------------------------------------------------- log(x)