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

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

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*}