sin(x)*log(2*x)
d --(sin(x)*log(2*x)) dx
Apply the product rule:
; to find :
The derivative of sine is cosine:
; to find :
Let .
The derivative of is .
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 answer is:
sin(x) ------ + cos(x)*log(2*x) x
sin(x) 2*cos(x) - ------ - log(2*x)*sin(x) + -------- 2 x x
3*sin(x) 3*cos(x) 2*sin(x) -cos(x)*log(2*x) - -------- - -------- + -------- x 2 3 x x