*Notes to a video lecture on http://www.unizor.com*

__Partial Derivatives - Examples__

*Example 1*

Let

**z=√x·y**Then

*∂*

**z**/∂**x**= assuming**y**constant =**y/(2√x·y)***∂*

**z**/∂**y**= assuming**x**constant =**x/(2√x·y)***Example 2*

Let

**z=e**^{x·y}Then

*∂*

**z**/∂**x**= assuming**y**constant =**y·e**^{x·y}*∂*

**z**/∂**y**= assuming**x**constant =**x·e**^{x·y}*Example 3*

Let

**z=1/(x²+y²)**Then

*∂*

**z**/∂**x**= assuming**y**constant =**−2x/(x²+y²)²***∂*

**z**/∂**y**= assuming**x**constant =**−2y/(x²+y²)²***Example 4*

Let

**z=sin(x)/y²**Then

*∂*

**z**/∂**x**= assuming**y**constant =**cos(x)/y²***∂*

**z**/∂**y**= assuming**x**constant =**−2sin(x)/y³***Example 5*

Let

**z=arctan(x√y)**Then

*∂*

**z**/∂**x**= assuming**y**constant =**√y/(1+x²·y)***∂*[

**z**/∂**y**= assuming**x**constant =**x/***]*

**2√y(1+x²·y)***Example 6*

Let

**z=y**^{x}Then

*∂*

**z**/∂**x**= assuming**y**constant =**y**^{x}·ln(y)*∂*

**z**/∂**y**= assuming**x**constant =**x·y**^{x−1}
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