Implicit differentiation is used when&nbsp;$x$ and $y$ are mixed together in an equation and it’s difficult (or impossible) to make $y$ the subject. Key Idea: Differentiate both sides of the equation with respect to $x$, treating $y$ as a function of $x$ and applying the chain rule to include the derivative of $y$, $\frac{\mathrm{d}y}{\mathrm{d}x}$. Use the product rule of differentiation, where necessary. For example: Given a circle with equation $\begin{matrix}
 {{x}^{2}}+{{y}^{2}}=25 \\
\end{matrix}$, find an expression for&nbsp;$\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$.

**Implicit differentiation** is used when $x$ and $y$ are mixed together in an equation and it’s difficult (or impossible) to make $y$ the subject.
Key Idea:
Differentiate both sides of the equation with respect to $x$, treating $y$ as a function of $x$ and applying the chain rule to include the derivative of $y$, $\frac{\mathrm{d}y}{\mathrm{d}x}$. Use the product rule of differentiation, where necessary.
For example:
Given a circle with equation $\begin{matrix}
   {{x}^{2}}+{{y}^{2}}=25  \\
\end{matrix}$, find an expression for $\frac{\mathrm{d}y}{\mathrm{d}x}$ in terms of $x$ and $y$.


Implicit Differentiation (Optional)

Implicit Differentiation (Optional)