Partial Derivatives: Practice Problems and Solutions
Introduction
Partial derivatives are essential tools for understanding and working with multivariable functions. Here is a set of practice problems to help you develop your skills in finding first-order partial derivatives.
Practice Problems
1. Find the partial derivatives of f(x, y) = x^2 + y^3. 2. Find the partial derivatives of g(x, y, z) = xy + yz + xz. 3. Find the partial derivatives of h(u, v, w) = u^2v + vw^2. 4. Find the partial derivatives of p(x, y, z) = e^(x + y + z). 5. Find the partial derivatives of q(x, y, z) = ln(x^2 + y^2 + z^2). 6. Find the partial derivatives of r(x, y, z) = sin(xyz). 7. Find the partial derivatives of s(x, y, z) = cos(x^2 + y^2 + z^2). 8. Find the partial derivatives of t(x, y, z) = tan(xyz).
Solutions
The solutions to these practice problems can be found in the Calculus III notes, Chapter 133. By working through these problems and referencing the notes, you can improve your understanding of partial derivatives and enhance your math skills.
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