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To calculate the partial derivative of a function choose the variable with respect to which you want to take the partial derivative, and treat all the other variables as constant. Differentiate the function with respect to the chosen variable, using the rules of differentiation.
What are the rules of partial derivatives?
Partial derivatives follow the sane rules as derivatives: the sum rule, the difference rule, the product rule, the quotient rule, and the chain rule.
What is the sum rule of partial derivatives?
The sum rule of partial derivatives is a technique for calculating the partial derivative of the sum of two functions. It states that if f(x,y) and g(x,y) are both differentiable functions, then:
∂(f+g)/∂x = ∂f/∂x + ∂g/∂x
∂(f+g)/∂y = ∂f/∂y + ∂g/∂y
What is the difference rule of partial derivatives?
The difference rule of partial derivatives is a technique for calculating the partial derivative of the difference of two functions. It states that if f(x,y) and g(x,y) are both differentiable functions, then:
∂(f-g)/∂x = ∂f/∂x - ∂g/∂x
∂(f-g)/∂y = ∂f/∂y - ∂g/∂y
What is the product rule of partial derivatives?
The product rule of partial derivatives is a technique for calculating the partial derivative of the product of two functions. It states that if f(x,y) and g(x,y) are both differentiable functions, then:
∂(fg)/∂x = f∂g/∂x + g∂f/∂x
∂(fg)/∂y = f∂g/∂y + g∂f/∂y
What is the quotient rule of partial derivatives?
The quotient rule of partial derivatives is a technique for calculating the partial derivative of the quotient of two functions. It states that if f(x,y) and g(x,y) are both differentiable functions and g(x,y) is not equal to 0, then:
∂(f/g)/∂x = (∂f/∂xg - f∂g/∂x)/g^2
∂(f/g)/∂y = (∂f/∂yg - f∂g/∂y)/g^2
What is the chain rule of partial derivatives?
The chain rule of partial derivatives is a technique for calculating the partial derivative of a composite function. It states that if f(x,y) and g(x,y) are both differentiable functions, and y is a function of x (i.e. y = h(x)), then: ∂f/∂x = ∂f/∂y * ∂y/∂x
What is the partial derivative of a function?
The partial derivative of a function is a way of measuring how much the function changes when you change one of its variables, while holding the other variables constant.
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