cos(x) ------ 2 5*x
cos(x)/((5*x^2))
Apply the quotient rule, which is:
and .
To find :
The derivative of cosine is negative sine:
To find :
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:
Now plug in to the quotient rule:
Now simplify:
The answer is:
1 2*cos(x) - ----*sin(x) - -------- 2 3 5*x 5*x
4*sin(x) 6*cos(x) -cos(x) + -------- + -------- x 2 x ----------------------------- 2 5*x
24*cos(x) 18*sin(x) 6*cos(x) - --------- - --------- + -------- + sin(x) 3 2 x x x ------------------------------------------- 2 5*x