Example 1 Find all of the first order partial derivatives for the following
functions.
1.
2.
3.
4.
f(x,y)=x4+6√ y −10f(x,y)=x4+6y−10
w=x2y−10y2z3+43x−7tan(4y)w=x2y−10y2z3+43x−7tan⁡(4y)
h(s,t)=t7ln(s2)+9t3−7√ s4 h(s,t)=t7ln⁡(s2)+9t3−s47
f(x,y)=cos(4x)ex2y−5y3f(x,y)=cos⁡(4x)ex2y−5y3
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a f(x,y)=x4+6√ y −10f(x,y)=x4+6y−10 Show Solution
b w=x2y−10y2z3+43x−7tan(4y)w=x2y−10y2z3+43x−7tan⁡(4y) Show
Solution
c h(s,t)=t7ln(s2)+9t3−7√ s4 h(s,t)=t7ln⁡(s2)+9t3−s47 Show Solution
d f(x,y)=cos(4x)ex2y−5y3f(x,y)=cos⁡(4x)ex2y−5y3 Show Solution
Example 2 Find all of the first order partial derivatives for the following
functions.
1. z=9uu2+5vz=9uu2+5v
2. g(x,y,z)=xsin(y)z2g(x,y,z)=xsin⁡(y)z2
3. z=√ x2+ln(5x−3y2) z=x2+ln⁡(5x−3y2)
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a z=9uu2+5vz=9uu2+5v Show Solution
b g(x,y,z)=xsin(y)z2g(x,y,z)=xsin⁡(y)z2 Show Solution
c z=√ x2+ln(5x−3y2) z=x2+ln⁡(5x−3y2) Show Solution