# How to calculate nonlinear simultaneous equation where the 1st derivative =0?

The equations should be solved

$h(x,y)=x+\frac{\partial f(x,y)}{\partial x}$-inp_x, $~$$g(x,y)=y+\frac{\partial f(x,y)}{\partial y}$-inp_y, where inp_x(y) is a constant.

I tried to solve the equations by newton raphson (NR) methods for root finding.

But, I couldn't solve the equations where $\frac{\partial f(x,y)}{\partial x}=0$ and/or $\frac{\partial f(x,y)}{\partial y}=0$.

For a $\frac{\partial f}{\partial x}=0$ and $\frac{\partial f}{\partial y}\neq0$ system, am I right to calculate

1stly $h(x,y)$ as optimization problem (i.e., finding extrema point),

2ndly substituted optimized y_value into $g(x,y)$, and 3rdly solve $g(x,y)$ by NR mothods?

If I am not, please tell me how to solve the equations. Thanks in advance.

• Welcome to StackExchange. Please see this tutorial for typesetting Maths nicely on this site. Please use it to rewrite your question so it is easier to read – lioness99a May 16 '17 at 9:24
• Thanks for your comment. My considering algorithm above doesn't work well (Maybe hessian matrix in my code is wrong). For now, I' ll check the matrix. – takeshi May 17 '17 at 1:46