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Gradient of the quotient of two scalar point functions

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Important Formulas and their Explanations (V):
Gradient, Divergence and Curl
Gradient of the quotient of two scalar point functions

Gradient of the quotient of two scalar point functions.

If f and g are two scalar point functions, then
grad (f/g) = ( g grad f - f grad g )/g^2,

that is, gradient of (f/g) = ( g gradient of f - f gradient of g )/g^2,

that is, (f/g) = (g f - f g)/g^2

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This solution is comprised of a detailed explanation of the gradient of the quotient of two scalar point functions.
It contains step-by-step explanation for the following problem:

Gradient of the quotient of two scalar point functions.

If f and g are two scalar point functions, then
grad (f/g) = ( g grad f - f grad g )/g^2,

that is, gradient of (f/g) = ( g gradient of f - f gradient of g )/g^2,

that is, (f/g) = (g f - f g)/g^2

Solution contains detailed step-by-step explanation.

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Important Formulas and their Explanations (V):
Gradient, Divergence and Curl
Gradient of the quotient of two scalar point functions

...

Solution provided by:
Thokchom Sarojkumar Sinha, MSc
Education
  • BSc, Manipur University
  • MSc, Kanpur University
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