2 4*cot(x) + 12*x
d / 2\ --\4*cot(x) + 12*x / dx
Differentiate term by term:
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 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 is:
Now simplify:
The answer is:
/ / 2 \ \ 8*\3 + \1 + cot (x)/*cot(x)/
/ 2 \ / 2 \ -8*\1 + cot (x)/*\1 + 3*cot (x)/