Get the solution to "Find both first partial derivatives. z=cos⁡xy"

College
Calculus and Analysis
Differential Calculus
Derivatives

e1s2kat26

Answered question

2021-04-26

Find both first partial derivatives.

z = \cos x y

Answer & Explanation

Arnold Odonnell

Skilled2021-04-28Added 109 answers

Step 1 Let's determine the partial derivatives of the specified function.
We have:
$z = \cos x y$
Step 2
$z = \cos x y$
$\frac{\partial z}{\partial x} = - \sin (x y) \cdot y$
$\frac{\partial z}{\partial x} = - y \cdot \sin (x y)$
$\frac{\partial z}{\partial y} = - \sin (x y) \cdot x$
$\frac{\partial z}{\partial y} = - x \sin (x y)$
Step 3 Answer
$\frac{\partial z}{\partial x} = - y \sin (x y)$
$\frac{\partial z}{\partial y} = - x \sin (x y)$

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