/ _______\ sin(2*x)*log\\/ x - 1 /
sin(2*x)*log(sqrt(x - 1))
Apply the product rule:
; to find :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
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:
The result of the chain rule is:
; to find :
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
Let .
Apply the power rule: goes to
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 of the chain rule is:
The result is:
Now simplify:
The answer is:
sin(2*x) / _______\ --------- + 2*cos(2*x)*log\\/ x - 1 / 2*(x - 1)
/ ________\ 2*cos(2*x) sin(2*x) - 4*log\\/ -1 + x /*sin(2*x) + ---------- - ----------- -1 + x 2 2*(-1 + x)
sin(2*x) / ________\ 6*sin(2*x) 3*cos(2*x) --------- - 8*cos(2*x)*log\\/ -1 + x / - ---------- - ---------- 3 -1 + x 2 (-1 + x) (-1 + x)