# 1.7 Partial Derivatives

**The use of calculators or other technologies are strictly prohibited for this assignment.**

## 1 Intro to Partial Derivatives

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Consider $f(x) = x^2 y + \sin(y)$.

a) Find $\frac{\partial f}{\partial x}$.

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b) What is the partial derivative of $f$ with respect to $x$, evaluated at (1, 1)?

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c) Find $\frac{\partial f}{\partial y}$.

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d) What is the partial derivative of $f$ with respect to $x$, evaluated at (1, 0)?

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## 2 More Partial Derivatives

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Consider $f(x) = x^{3/4}y^{1/4}$.

a) Find $\frac{\partial f}{\partial x}$.

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b) Find $\frac{\partial f}{\partial y}$.

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c) Simplify $\frac{\frac{\partial f}{\partial x}}{\frac{\partial f}{\partial y}}$.

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Consider $f(x) = \frac{3}{4} \log(x) + \frac{1}{4} \log(y)$

d) Find $\frac{\partial f}{\partial x}$.

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e) Find $\frac{\partial f}{\partial y}$.

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f) Find $\frac{\frac{\partial f}{\partial x}}{\frac{\partial f}{\partial y}}$.

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