Resolved: "Calculate all four second-order partial derivatives of f(x,y)=(5x+4y)ey"

College
Calculus and Analysis
Differential Calculus
Derivatives

keche0b

Answered question

2021-12-09

Calculate all four second-order partial derivatives of

f (x, y) = (5 x + 4 y) e^{y}

Answer & Explanation

Dawn Neal

Beginner2021-12-10Added 35 answers

Given:
$f (x, y) = (5 x + 4 y) e^{y}$
$f_{x} = 5 e^{y}$
$f_{x x} = 0$
$f_{x y} = 5 e^{y}$
$f_{y} = 5 x e^{y} + 4 y e^{y} + 4 e^{y}$
$f_{y y} = 5 x e^{y} + 4 e^{y} + 4 e^{y} + 4 y e^{y}$
$f_{y y} = 5 x e^{y} + 8 e^{y} + 4 y e^{y}$
$f_{y x} = 5 e^{y}$

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