If x^2+y^2+ y=4, then the value of d^2ydx^2 at the point (-2,0) is

Question

If $x^2+y^2+\sin y=4$, then the value of $\dfrac{d^2y}{dx^2}$ at the point $(-2,0)$ is

Accepted Answer

Differentiating: $2x+(2y+\cos y)\dfrac{dy}{dx}=0$. At $(-2,0)$: $-4+1\cdot y'=0\Rightarrow y'=4$.

Differentiating again: $2+(2-\sin y)(y')^2+(2y+\cos y)y''=0$. At $(-2,0)$ with $y'=4$: $2+2\cdot16+1\cdot y''=0\Rightarrow y''=-34$.

Solutions · 1