<s>[INST] How to rewrite $\frac{d}{d(x+c)}$? I would like to know how to rewrite the following equations:
$$
\frac{d (f(x))}{d(x+c)} =0\\
\frac{d^2 (f(x))}{d(x+c)^2} =0\\
$$
Here $x$ is a variable, $c$ is a constant and $f(x)$ is a function of x.
I would also like to know the reasoning behind the answer.
 [/INST] $$\frac { d }{ dx } \left( f\left( x \right) \left( x+c \right) ^{ -1 } \right) =0\\ \frac { df\left( x \right)  }{ dx } \left( x+c \right) ^{ -1 }+f\left( x \right) \frac { d\left( \left( x+c \right) ^{ -1 } \right)  }{ dx } =0\\ \frac { df\left( x \right)  }{ dx } \frac { 1 }{ \left( x+c \right)  } -f\left( x \right) \frac { 1 }{ { \left( x+c \right)  }^{ 2 } } =0$$
</s>