Implicit differentiation

In calculus, implicit differentiation is a method of finding the derivative of an implicit function using the chain rule. To differentiate an implicit function $y (x)$ , defined by an equation $R (x, y) = 0$ , it is not generally possible to solve it explicitly for $y$ and then differentiate it. Instead, one can totally differentiate $R (x, y) = 0$ with respect to $x$ and $y$ and then solve the resulting linear equation for $/* start https://en.wikipedia.org/ */ .mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px} /* end https://en.wikipedia.org/ */ ⁠dy/dx⁠$ , to get the derivative explicitly in terms of $x$ and $y$ . Even when it is possible to explicitly solve the original equation, the formula resulting from total differentiation is, in general, much simpler and easier to use.