In real-world applications, derivatives help us understand how a dependent variable changes with respect to an independent variable. **Example:** So if you are a car producer, you might want to know how the weight $w$ of your car changes, when changing the thickness $t$ of the material it is produced of. This is expressed as: $ \frac{dw}{dt} \quad (\text{change in} \:w \: \text{with respect to}\: t)$ **Partial Derivative:** When dealing with multivariate functions (i.e. a function $f(x,y,z)$ has multiple independent variables), we use partial derivatives to analyze how the dependent variable changes with respect to one independent variable while keeping the others constant. Note: - We use $d$ for derivatives of univariate functions - We use $\partial$ for partial derivatives of multivariate functions **Example:** Consider the following multivariate function.. $ f(x,y,z)=\sin(x)*e^{yz^2} $ We can compute partial derivatives of how the function output changes, when only changing one of the 3 inputs. $ \begin{aligned} \frac{\partial f}{\partial x}&=\cos(x)* e^{yz^2} &&\impliedby \sin(x)*c \\ \frac{\partial f}{\partial y}&=\sin(x)*e^{yz^2}*z^2 &&\impliedby c*e^{yc} \\ \frac{\partial f}{\partial z}&=\sin(x)*e^{yz^2}*2yz &&\impliedby c*e^{cz^2} \\ \end{aligned} $