Second-Order Partial Derivatives
Similar to the computation of second-order derivatives for functions of single variables, we can compute the same for functions of several variables.
For an example we consider the same function [Tex]z = x^2 + y^2 + 3xy [/Tex].
Case 1: We differentiate [Tex]\frac{\partial z}{\partial x} [/Tex] again with respect to ‘x’
Case 2: We differentiate [Tex]\frac{\partial z}{\partial y} [/Tex] again with respect to ‘y’
Case 3: We differentiate [Tex]\frac{\partial z}{\partial x} [/Tex] again with respect to ‘y’
Case 4: We differentiate [Tex]\frac{\partial z}{\partial y} [/Tex] again with respect to ‘x’
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Partial Derivatives in Engineering Mathematics
Partial Derivatives in Engineering Mathematics: A function is like a machine that takes some input and gives a single output. For example, y = f(x) is a function in ‘x’. Here, we say ‘x’ is the independent variable and ‘y’ is the dependent variable as the value of ‘y’ depends on ‘x’.
Some examples of functions are:
- f(x) = x2 + 3 is an algebraic function.
- ex is the exponential function.
- sin(x), cos(x), tan(x),…etc. are all trigonometric functions.
Now, all these functions are functions of a single variable, i.e. there is only one independent variable.
Table of Content
- Partial Derivatives in Engineering Mathematics
- Partial Derivatives Examples
- Geometrical Interpretation of Partial Derivative
- Calculation of Partial Derivatives of a Function
- Second-Order Partial Derivatives
- Applications of Partial Derivatives in Engineering