Question

Find $f_{x}$ and $f_{y}$ when $f(x, y)=y^{8}+2 x^{6}+2 x y$.

   Find $f_{x}$ and $f_{y}$ when $f(x, y)=y^{8}+2 x^{6}+2 x y$.

Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle… 3rd Edition

Chapter 15, Problem 4

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Solved by Expert Jake Zanazzi

05/25/2020

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This means we treat $y$ as a constant. Show more…

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Find $f_{x}$ and $f_{y}$ when $f(x, y)=y^{8}+2 x^{6}+2 x y$.

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Key Concepts

Product Rule

The product rule is a method used to differentiate products of two functions. It states that the derivative of a product is the first function times the derivative of the second function plus the second function times the derivative of the first function. This rule becomes particularly important when dealing with terms that include products of variables in a multivariable setting.

Partial Differentiation

Partial differentiation involves finding the derivative of a function with several variables with respect to one variable while treating the other variables as constants. It is used to understand how the function changes as one variable changes, and it is fundamental in multivariable calculus.

Power Rule

The power rule is a basic differentiation technique stating that the derivative of x^n is n*x^(n-1). This rule is applied to terms in a function that consist of a variable raised to a power, making it a crucial tool in computing derivatives in both single-variable and multivariable calculus.

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