Find the derivative in term of $x$ and $y$.

Question

$\frac{\mathrm{d}y}{\mathrm{d}x} = 3x + 2y + 1$

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 $y$.

Answer 1

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.

Answer 2

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