4 ______________ \/ 1 + sin(6*x)
d /4 ______________\ --\\/ 1 + sin(6*x) / dx
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Differentiate term by term:
The derivative of the constant is zero.
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:
The result is:
The result of the chain rule is:
The answer is:
3*cos(6*x) ------------------- 3/4 2*(1 + sin(6*x))
/ 2 \ | 3*cos (6*x) | -9*|---------------- + sin(6*x)| \4*(1 + sin(6*x)) / -------------------------------- 3/4 (1 + sin(6*x))
/ 2 \ | 9*sin(6*x) 21*cos (6*x) | 27*|-2 + ---------------- + -----------------|*cos(6*x) | 2*(1 + sin(6*x)) 2| \ 8*(1 + sin(6*x)) / ------------------------------------------------------- 3/4 (1 + sin(6*x))