# What is the Difference Between Partial and Total Derivative?

The difference between a partial derivative $$\frac{\partial f(x,y)}{\partial x}$$ to $$x$$ and a total derivative $$\frac{\text{d}f(x,y)}{\text{d}x}$$ to $$x$$ is that in the partial derivative it is assumed that $$y$$ is independent of $$x$$.
• In the partial derivative $$\frac{\partial f(x,y)}{\partial x}$$ $$y$$ is kept constant.
• The total derivative $$\frac{\text{d}f(x,y(x))}{\text{d}x}$$ does NOT assume that $$y$$ is constant. The change of $$x$$ also affects $$y$$.