x*tan(x)
d --(x*tan(x)) dx
Apply the product rule:
; to find :
Apply the power rule: goes to
; 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:
The result is:
Now simplify:
The answer is:
/ 2 \ x*\1 + tan (x)/ + tan(x)
/ 2 / 2 \ \ 2*\1 + tan (x) + x*\1 + tan (x)/*tan(x)/
/ 2 \ / / 2 \\ 2*\1 + tan (x)/*\3*tan(x) + x*\1 + 3*tan (x)//