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Elementary partial derivative problems

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  1. Let $h(t,s)=\left(- 2 s + 3\right) \ln{\left (5 c t \right )}$, where $c$ is a positive parameter. Calculate $\pdiff{ h }{ t }$ and $\pdiff{ h }{ s }$.
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  2. Let $h(c,v)$ be your risk of heart disease as a function of the amount of cholesterol you eat $c$ and the amount of vegetables you eat $v$.
    1. Describe what the quantity $\pdiff{ h }{ v }$ means.
    2. Let $h(c,v)= 8 e^{2 c - 6 v}$. Calculate $\pdiff{ h }{ c }$ and $\pdiff{ h }{ v }$.

  3. Let $f(y,s)=\left(- 8 s + 3\right) \left(- 8 y - 1\right)$. Calculate $\pdiff{ f }{ y }$ and $\pdiff{ f }{ s }$.
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  4. Let $w(u,v)=10 u^{2} + 8 u v - 8 v^{2}$. Calculate $\pdiff{ w }{ u }$ and $\pdiff{ w }{ v }$.
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  5. Let $x(w,t)=\left(- 7 w - 3\right) e^{- 8 t + 7}$. Calculate $\pdiff{ x }{ w }$ and $\pdiff{ x }{ t }$.
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Math 1241, Fall 2013