tan(x)*log(x)
d --(tan(x)*log(x)) dx
Apply the product rule:
; to find :
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
The derivative of cosine is negative sine:
Now plug in to the quotient rule:
; to find :
The derivative of is .
The result is:
Now simplify:
The answer is:
tan(x) / 2 \ ------ + \1 + tan (x)/*log(x) x
/ 2 \ tan(x) 2*\1 + tan (x)/ / 2 \ - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x) 2 x x
/ 2 \ / 2 \ 3*\1 + tan (x)/ 2*tan(x) / 2 \ / 2 \ 6*\1 + tan (x)/*tan(x) - --------------- + -------- + 2*\1 + tan (x)/*\1 + 3*tan (x)/*log(x) + ---------------------- 2 3 x x x