4 3 3*x - 4*x ----------- 5*x + 1
/ 4 3\ d |3*x - 4*x | --|-----------| dx\ 5*x + 1 /
Apply the quotient rule, which is:
and .
To find :
Differentiate term by term:
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 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:
To find :
Differentiate term by term:
The derivative of the constant is zero.
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 plug in to the quotient rule:
Now simplify:
The answer is:
2 3 / 4 3\ - 12*x + 12*x 5*\3*x - 4*x / --------------- - --------------- 5*x + 1 2 (5*x + 1)
/ 2 \ | 60*x*(-1 + x) 25*x *(-4 + 3*x)| 2*x*|-12 + 18*x - ------------- + ----------------| | 1 + 5*x 2 | \ (1 + 5*x) / --------------------------------------------------- 1 + 5*x
/ 3 2 \ | 125*x *(-4 + 3*x) 30*x*(-2 + 3*x) 300*x *(-1 + x)| 6*|-4 + 12*x - ----------------- - --------------- + ---------------| | 3 1 + 5*x 2 | \ (1 + 5*x) (1 + 5*x) / --------------------------------------------------------------------- 1 + 5*x