/ ___\ ________ sin\\/ x / - \/ cos(x)
sin(sqrt(x)) - sqrt(cos(x))
Differentiate term by term:
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
Apply the power rule: goes to
The result of the chain rule is:
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
The derivative of cosine is negative sine:
The result of the chain rule is:
So, the result is:
The result is:
The answer is:
/ ___\ cos\\/ x / sin(x) ---------- + ------------ ___ ________ 2*\/ x 2*\/ cos(x)
2 / ___\ / ___\ ________ sin (x) sin\\/ x / cos\\/ x / 2*\/ cos(x) + --------- - ---------- - ---------- 3/2 x 3/2 cos (x) x -------------------------------------------------- 4
/ ___\ / ___\ / ___\ 3 cos\\/ x / 2*sin(x) 3*sin\\/ x / 3*cos\\/ x / 3*sin (x) - ---------- + ---------- + ------------ + ------------ + --------- 3/2 ________ 2 5/2 5/2 x \/ cos(x) x x cos (x) ------------------------------------------------------------------- 8