Expert Answer to "Find both first partial derivatives. z=xy"

College
Calculus and Analysis
Differential Calculus
Derivatives

Tolnaio

Answered question

2021-02-14

Find both first partial derivatives.

z = x \sqrt{y}

Answer & Explanation

hajavaF

Skilled2021-02-16Added 90 answers

Step 1
Here given
$z = x \sqrt{y}$
Step 2
Thus
$\frac{\partial z}{\partial x} = \frac{\partial}{\partial x} (x \sqrt{y})$
$= \sqrt{y}$
and
$\frac{\partial z}{\partial y} = \frac{\partial}{\partial y} (x \sqrt{y})$
$= x \times \frac{1}{2} \times {(y)}^{\frac{- 1}{2}}$
$= \frac{x}{2 \sqrt{y}}$

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