cot(x) sin(x) + ------ 2
sin(x) + cot(x)/2
Differentiate term by term:
The derivative of sine is cosine:
The derivative of a constant times a function is the constant times the derivative of the function.
There are multiple ways to do this derivative.
Rewrite the function to be differentiated:
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
The derivative of sine is cosine:
To find :
The derivative of cosine is negative sine:
Now plug in to the quotient rule:
The result of the chain rule is:
Rewrite the function to be differentiated:
Apply the quotient rule, which is:
and .
To find :
The derivative of cosine is negative sine:
To find :
The derivative of sine is cosine:
Now plug in to the quotient rule:
So, the result is:
The result is:
Now simplify:
The answer is:
2 1 cot (x) - - - ------- + cos(x) 2 2
/ 2 \ -sin(x) + \1 + cot (x)/*cot(x)
/ 2 \ |/ 2 \ 2 / 2 \ | -\\1 + cot (x)/ + 2*cot (x)*\1 + cot (x)/ + cos(x)/