Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 15 - Differentiation in Several Variables - 15.5 The Gradient and Directional Derivatives - Exercises - Page 801: 5


$$\nabla f =\left\langle-2x\sin \left(x^{2}+y\right),-\sin \left(x^{2}+y\right) \right\rangle$$

Work Step by Step

Given $$ f(x, y)=\cos \left(x^{2}+y\right) $$ Then \begin{align*} \nabla f&=\left\langle\frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right\rangle\\ &=\left\langle-2x\sin \left(x^{2}+y\right),-\sin \left(x^{2}+y\right) \right\rangle \end{align*}
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.