TITLE: Find the derivative in term of $x$ and $y$.
QUESTION [6 upvotes]: $\frac{\mathrm{d}y}{\mathrm{d}x} = 3x + 2y + 1$ 
Find $\frac{\mathrm{d}^2 y}{\mathrm{d}x^2}$ in term of $x$ and $y$. 
I get $3+2y^{\prime}$ for the answer.  Lost upon how to get the answer in terms of $x$ and $y$.

REPLY [7 votes]: Substitute the known value of $y'=\frac{dy}{dx}$ in your expression that (almost) reads $\frac{d^2y}{dx^2}=3+2\frac{dy}{dx}$.

REPLY [7 votes]: You did all the work (the hard part)!
$$\dfrac {d^2y}{dx^2} = 3+2y^{\prime} = 3 + 2\cdot \dfrac {dy}{dx} = 3 + 2(3x + 2y + 1)$$
Simplify...you're done.