2 2 tan (x) - cot (x)
d / 2 2 \ --\tan (x) - cot (x)/ dx
Differentiate term by term:
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:
The derivative of a constant times a function is the constant times the derivative of the function.
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
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 :
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:
The result of the chain rule is:
So, the result is:
The result is:
Now simplify:
The answer is:
/ 2 \ / 2 \ \2 + 2*tan (x)/*tan(x) - \-2 - 2*cot (x)/*cot(x)
/ 2 2 \ |/ 2 \ / 2 \ 2 / 2 \ 2 / 2 \| 2*\\1 + tan (x)/ - \1 + cot (x)/ - 2*cot (x)*\1 + cot (x)/ + 2*tan (x)*\1 + tan (x)//
/ 2 2 \ | 3 / 2 \ 3 / 2 \ / 2 \ / 2 \ | 8*\cot (x)*\1 + cot (x)/ + tan (x)*\1 + tan (x)/ + 2*\1 + cot (x)/ *cot(x) + 2*\1 + tan (x)/ *tan(x)/