Partial derivative (English)
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Definition (advanced level)
If f(x, y) is a function of both x and y, then the partial derivative of f with respect to x, written [(∂f)/(∂x)], is:
This is equivalent to differentiating with respect to x and treating y as though it were a constant. It can also be written fx.
For example, if f(x, y) = x2 + xy + 2 y2,
then [(∂f)/(∂x)] = 2 x + y
We can define partial derivatives with respect to z, and of functions of three or more variables, in the same way.
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This is equivalent to differentiating with respect to x and treating y as though it were a constant. It can also be written fx.
For example, if f(x, y) = x2 + xy + 2 y2,
then [(∂f)/(∂x)] = 2 x + y
We can define partial derivatives with respect to z, and of functions of three or more variables, in the same way.
Relations
- broader:
- (en) Derivative
- narrower:
- (en) Higher partial derivative
- (en) Mixed partial derivative
- references:
- (en) Multivariable calculus
- referenced:
- (en) Contravariant tensor
- (en) Covariant tensor
- (en) Differential operator
- (en) Directional derivative
- (en) Exact differential
- (en) Extremum
- (en) Grad
- (en) Hessian matrix
- (en) Jacobian matrix
- (en) Normal line
- (en) Partial differential equation
- (en) Stationary point
- (en) Total derivative
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