sin(x) ---------- log(x) + 1
sin(x)/(log(x) + 1)
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
Differentiate term by term:
The derivative of the constant is zero.
The derivative of is .
The result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
cos(x) sin(x) ---------- - --------------- log(x) + 1 2 x*(log(x) + 1)
/ 2 \ |1 + ----------|*sin(x) 2*cos(x) \ 1 + log(x)/ -sin(x) - -------------- + ----------------------- x*(1 + log(x)) 2 x *(1 + log(x)) -------------------------------------------------- 1 + log(x)
/ 3 3 \ 2*|1 + ---------- + -------------|*sin(x) / 2 \ | 1 + log(x) 2| 3*|1 + ----------|*cos(x) 3*sin(x) \ (1 + log(x)) / \ 1 + log(x)/ -cos(x) + -------------- - ----------------------------------------- + ------------------------- x*(1 + log(x)) 3 2 x *(1 + log(x)) x *(1 + log(x)) ------------------------------------------------------------------------------------------------ 1 + log(x)