Consider a function f(x, y, z) given by

f(x, y, z) = (x² + y² – 2z²)(y² + z²)

The partial derivative of this function with respect to x at the point x = 2, y = 1 and z = 3 is _______

Concept:

In Partial Differentiation, all variables are considered as a constant except the independent derivative variable i.e If f(x,y,z) is a function, then its partial derivative with respect to x is calculated by keeping y and z as constant.

Calculation:

f(x, y, z) = (x² + y² – 2z²)(y² + z²)

$\frac{\partial f}{\partial x}=\left(2x\right)\left(y^2+z^2\right)$

At the point, x = 2, y = 1 and z = 3 is

$\frac{\partial f}{\partial x}=2\left(2\right)\left(1^2+3^2\right)=40$