1 1*------------ 4 __________ \/ sin(5*x)
d / 1 \ --|1*------------| dx| 4 __________| \ \/ sin(5*x) /
Apply the quotient rule, which is:
and .
To find :
The derivative of the constant is zero.
To find :
Let .
Apply the power rule: goes to
Then, apply the chain rule. Multiply by :
Let .
The derivative of sine is cosine:
Then, apply the chain rule. Multiply by :
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 of the chain rule is:
The result of the chain rule is:
Now plug in to the quotient rule:
The answer is:
-5*cos(5*x) ----------------------- 4 __________ 4*sin(5*x)*\/ sin(5*x)
/ 2 \ | 5*cos (5*x)| 25*|4 + -----------| | 2 | \ sin (5*x) / -------------------- 4 __________ 16*\/ sin(5*x)
/ 2 \ | 45*cos (5*x)| -125*|44 + ------------|*cos(5*x) | 2 | \ sin (5*x) / --------------------------------- 5/4 64*sin (5*x)