_______ \/ x - 2 *sin(3*x - 2)
sqrt(x - 2)*sin(3*x - 2)
Apply the product rule:
; to find :
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:
; to find :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
Differentiate term by term:
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 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(3*x - 2) _______ ------------ + 3*\/ x - 2 *cos(3*x - 2) _______ 2*\/ x - 2
________ 3*cos(-2 + 3*x) sin(-2 + 3*x) - 9*\/ -2 + x *sin(-2 + 3*x) + --------------- - ------------- ________ 3/2 \/ -2 + x 4*(-2 + x)
/ ________ 9*sin(-2 + 3*x) 3*cos(-2 + 3*x) sin(-2 + 3*x)\ 3*|- 9*\/ -2 + x *cos(-2 + 3*x) - --------------- - --------------- + -------------| | ________ 3/2 5/2| \ 2*\/ -2 + x 4*(-2 + x) 8*(-2 + x) /