Partial Derivative/Examples/x z^y

Example of Partial Derivative

Let $\map f {x, y, z} = x z^y$ be a real function of $3$ variables.

Then the partial derivative with respect to the $2$nd variable may be expressed as:

$\map {f_2} {x, y, z} = x z^y \ln z$

and because of the notation chosen, we have:

$\map {f_2} {r, s, t} = r t^s \ln t$

Sources

• 1961: David V. Widder: Advanced Calculus (2nd ed.) ... (previous) ... (next): $1$ Partial Differentiation: $\S 1$. Introduction: $1.1$ Partial Derivatives