Apply the product rule:
; to find :
The derivative of is itself.
; 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 x \1 + tan (x)/*e + e *tan(x)
/ 2 / 2 \ \ x \2 + 2*tan (x) + 2*\1 + tan (x)/*tan(x) + tan(x)/*e
/ 2 / 2 \ / 2 \ / 2 \ \ x \3 + 3*tan (x) + 2*\1 + tan (x)/*\1 + 3*tan (x)/ + 6*\1 + tan (x)/*tan(x) + tan(x)/*e