Monday, June 5, 2017
Unizor - Partial Derivatives - Examples
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=ex·y
Then
∂z/∂x = assuming y constant = y·ex·y
∂z/∂y = assuming x constant = x·ex·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=yx
Then
∂z/∂x = assuming y constant = yx·ln(y)
∂z/∂y = assuming x constant = x·yx−1
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