1 1*--------- 2 7*cot (x)
d / 1 \ --|1*---------| dx| 2 | \ 7*cot (x)/
Apply the quotient rule, which is:
and .
To find :
The derivative of the constant is zero.
To find :
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 :
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:
The result of the chain rule is:
So, the result is:
Now plug in to the quotient rule:
Now simplify:
The answer is:
1 / 2 \ - ---------*\-2 - 2*cot (x)/ 2 7*cot (x) ----------------------------- cot(x)
/ / 2 \\ / 2 \ | 3*\1 + cot (x)/| 2*\1 + cot (x)/*|-2 + ---------------| | 2 | \ cot (x) / -------------------------------------- 2 7*cot (x)
/ 2\ | / 2 \ / 2 \ | / 2 \ | 4*\1 + cot (x)/ 3*\1 + cot (x)/ | 8*\1 + cot (x)/*|1 - --------------- + ----------------| | 2 4 | \ cot (x) cot (x) / -------------------------------------------------------- 7*cot(x)