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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 2012 • Question 3

Question

Math 6510 • Differentiable Manifolds Fall 2012 • Question 3

Let \(g:\mathbb {R}^3\to \mathbb {R}^3\) be the function \(g(x,y,z)=(x^2y,3xz,y+z)\). Find \(D_{(2,3,5)}g:\mathbb {R}^3\to \mathbb {R}^3\), the derivative of \(g\) at the point \((2,3,5)\).

Raw LaTeX

Let \(g:\R^3\to\R^3\) be the function \(g(x,y,z)=(x^2y,3xz,y+z)\). Find
\(D_{(2,3,5)}g:\R^3\to\R^3\), the derivative of \(g\) at the point \((2,3,5)\).

Topic Tags

Tangent Spaces and Differential Maps