___ \/ x *sin(x + 6)
sqrt(x)*sin(x + 6)
Apply the product rule:
; to find :
Apply the power rule: goes to
; to find :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
Differentiate term by term:
Apply the power rule: goes to
The derivative of the constant is zero.
The result is:
The result of the chain rule is:
The result is:
Now simplify:
The answer is:
___ sin(x + 6) \/ x *cos(x + 6) + ---------- ___ 2*\/ x
cos(6 + x) ___ sin(6 + x) ---------- - \/ x *sin(6 + x) - ---------- ___ 3/2 \/ x 4*x
___ 3*sin(6 + x) 3*cos(6 + x) 3*sin(6 + x) - \/ x *cos(6 + x) - ------------ - ------------ + ------------ ___ 3/2 5/2 2*\/ x 4*x 8*x