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.