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College
Calculus and Analysis
Differential Calculus
Derivatives

EunoR

Answered question

2021-03-30

Find the four second partial derivatives of the following functions.

f (x, y) = e^{2 x y}

Answer & Explanation

Laaibah Pitt

Skilled2021-04-01Added 98 answers

Step 1
To find the four second partial derivatives of the given function.
Step 2
given function is
$f (x, y) = e^{2 x y}$
$f_{x} (x, y) = e^{2 x y} .2 y$
$f_{x x} (x, y) = 2 y \frac{d}{d x} (e^{2 x y})$
$= 4 y^{2} e^{2 x y}$
$f_{y} (x, y) = e^{2 x y} .2 x$
$f_{y y} (x, y) = 4 x^{2} . e^{2 x y}$
$f_{y x} (x, y) = 2 \frac{d}{d x} (e^{2 x y} . x)$
$= 2 e^{2 x y} (2 x y + 1)$
$f_{x y} (x, y) = 2 \frac{d}{d x} (e^{2 x y} . y)$
$= 2 e^{2 x y} (2 x y + 1)$

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