The gradient of the function <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle f(x,y)=-(\cos ^{2}(x)+\cos ^{2}(y))^{2}}"><semantics><mrow class="MJX-TeXAtom-ORD"><mstyle displaystyle="true" scriptlevel="0"><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo stretchy="false">)</mo><mo>=</mo><mo>−<!-- − --></mo><mo stretchy="false">(</mo><msup><mi>cos</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>⁡<!-- ⁡ --></mo><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo><mo>+</mo><msup><mi>cos</mi><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup><mo>⁡<!-- ⁡ --></mo><mo stretchy="false">(</mo><mi>y</mi><mo stretchy="false">)</mo><msup><mo stretchy="false">)</mo><mrow class="MJX-TeXAtom-ORD"><mn>2</mn></mrow></msup></mstyle></mrow><annotation encoding="application/x-tex">{\displaystyle f(x,y)=-(\cos ^{2}(x)+\cos ^{2}(y))^{2}}</annotation></semantics></math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/721655fae0259ea3ad31987fd1d4922432988d25" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -0.838ex; width:31.652ex; height:3.176ex;" alt="{\displaystyle f(x,y)=-(\cos ^{2}(x)+\cos ^{2}(y))^{2}}"></span> depicted as a vector field on the bottom plane.
<a href="//commons.wikimedia.org/wiki/User:MartinThoma" title="User:MartinThoma">MartinThoma</a>
<span class="int-own-work" lang="en">Own work</span>