Question

Find both first partial derivatives. z=x\sqrt{y}

Derivatives
ANSWERED
asked 2021-02-14
Find both first partial derivatives. \(\displaystyle{z}={x}\sqrt{{{y}}}\)

Expert Answers (1)

2021-02-16
Step 1
Here given
\(\displaystyle{z}={x}\sqrt{{{y}}}\)
Step 2
Thus
\(\displaystyle{\frac{{\partial{z}}}{{\partial{x}}}}={\frac{{\partial}}{{\partial{x}}}}{\left({x}\sqrt{{{y}}}\right)}\)
\(\displaystyle=\sqrt{{{y}}}\)
and
\(\displaystyle{\frac{{\partial{z}}}{{\partial{y}}}}={\frac{{\partial}}{{\partial{y}}}}{\left({x}\sqrt{{{y}}}\right)}\)
\(\displaystyle={x}\times{\frac{{{1}}}{{{2}}}}\times{\left({y}\right)}^{{{\frac{{-{1}}}{{{2}}}}}}\)
\(\displaystyle={\frac{{{x}}}{{{2}\sqrt{{{y}}}}}}\)
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