3 x *tan(x)
d / 3 \ --\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:
3 / 2 \ 2 x *\1 + tan (x)/ + 3*x *tan(x)
/ / 2 \ 2 / 2 \ \ 2*x*\3*tan(x) + 3*x*\1 + tan (x)/ + x *\1 + tan (x)/*tan(x)/
/ / 2 \ 3 / 2 \ / 2 \ 2 / 2 \ \ 2*\3*tan(x) + 9*x*\1 + tan (x)/ + x *\1 + tan (x)/*\1 + 3*tan (x)/ + 9*x *\1 + tan (x)/*tan(x)/