I think I wrote it wrong earlier
it should be
Find the derivative
y = (3x+2)/(x+1)
look at the solution given by Steve in
http://www.jiskha.com/display.cgi?id=1328927181
The answer to your question is 3
To find the derivative of y = (3x + 2)/(x + 1), you can use the quotient rule.
The quotient rule states that if you have a function in the form of f(x)/g(x), where f(x) and g(x) are both functions of x, then the derivative of y with respect to x is given by:
dy/dx = (g(x)*f'(x) - f(x)*g'(x))/[g(x)]^2
Let's apply this rule to find the derivative of y = (3x + 2)/(x + 1):
Step 1: Identify f(x) and g(x)
f(x) = 3x + 2
g(x) = x + 1
Step 2: Find f'(x) and g'(x)
f'(x) is the derivative of f(x), which is the derivative of 3x + 2. Since the derivative of a constant term (2 in this case) is zero, we can write:
f'(x) = d/dx(3x + 2) = 3
g'(x) is the derivative of g(x), which is the derivative of x + 1. The derivative of x with respect to x is 1, so we have:
g'(x) = d/dx(x + 1) = 1
Step 3: Apply the quotient rule formula to find dy/dx
Substituting the values we found into the quotient rule formula:
dy/dx = (g(x)*f'(x) - f(x)*g'(x))/[g(x)]^2
= [(x + 1)*(3) - (3x + 2)*(1)]/[(x + 1)^2]
= (3x + 3 - 3x - 2)/(x^2 + 2x + 1)
= 1/(x^2 + 2x + 1)
Therefore, the derivative of y = (3x + 2)/(x + 1) is dy/dx = 1/(x^2 + 2x + 1).