Find the derivative
y = 3x+2/x+1
See what happens if you don't use brackets ???
Jana, myself and Steve gave correct answers depending on which interpretation we give to your question.
http://www.jiskha.com/display.cgi?id=1328927181
Please use brackets.
Hmmm :-)
Actually, I was just looking at that again, and Jana's answer is incorrect. She said
3 + 2ln|x|
That is the derivative of 3x + the antiderivative of 2/x!
Still, her work indicated a possible interpretation of the syntax...
To find the derivative of the given function y = (3x+2)/(x+1), we will use the quotient rule. The quotient rule is used when we have a fraction where both the numerator and denominator are functions of x.
The quotient rule states that if we have a function y = u/v, then its derivative dy/dx is given by:
dy/dx = (v * du/dx - u * dv/dx) / v^2
In our case, u = (3x + 2) and v = (x + 1).
First, we need to find du/dx and dv/dx, the derivatives of the numerator and denominator, respectively.
du/dx = d/dx(3x + 2) = 3
dv/dx = d/dx(x + 1) = 1
Now, we can substitute these values into the quotient rule formula:
dy/dx = ((x + 1) * 3 - (3x + 2) * 1) / (x + 1)^2
To simplify this, let's expand and collect like terms in the numerator:
dy/dx = (3x + 3 - 3x - 2) / (x + 1)^2
= 1 / (x + 1)^2
Therefore, the derivative of y = (3x+2)/(x+1) is dy/dx = 1 / (x + 1)^2.