Apply the quotient rule, which is:
and .
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:
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:
The answer is:
3 2*(3*x + 5) ------- - ----------- 2*x - 1 2 (2*x - 1)
/ 2*(5 + 3*x)\ 4*|-3 + -----------| \ -1 + 2*x / -------------------- 2 (-1 + 2*x)
/ 2*(5 + 3*x)\ 24*|3 - -----------| \ -1 + 2*x / -------------------- 3 (-1 + 2*x)