3 sin(x) x*E + ------ log(x)
x*E^3 + sin(x)/log(x)
Differentiate term by term:
The derivative of a constant times a function is the constant times the derivative of the function.
Apply the power rule: goes to
So, the result is:
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
The derivative of is .
Now plug in to the quotient rule:
The result is:
Now simplify:
The answer is:
3 cos(x) sin(x) E + ------ - --------- log(x) 2 x*log (x)
sin(x) 2*cos(x) 2*sin(x) -sin(x) + --------- - -------- + ---------- 2 x*log(x) 2 2 x *log(x) x *log (x) ------------------------------------------- log(x)
6*sin(x) 6*sin(x) 2*sin(x) 3*sin(x) 3*cos(x) 6*cos(x) -cos(x) - ---------- - ---------- - --------- + -------- + --------- + ---------- 3 3 3 2 3 x*log(x) 2 2 2 x *log (x) x *log (x) x *log(x) x *log(x) x *log (x) --------------------------------------------------------------------------------- log(x)