cos(x) log(sin(x)) - ------ 4
log(sin(x)) - cos(x)/4
Differentiate term by term:
Let .
The derivative of is .
Then, apply the chain rule. Multiply by :
The derivative of sine is cosine:
The result of the chain rule is:
The derivative of a constant times a function is the constant times the derivative of the function.
The derivative of cosine is negative sine:
So, the result is:
The result is:
Now simplify:
The answer is:
sin(x) cos(x) ------ + ------ 4 sin(x)
2 cos(x) cos (x) -1 + ------ - ------- 4 2 sin (x)