Find a conservative vector field that has the indicated potential$$f(x,y,z)=\sin \left (x^2+y^2+z^2\right ).$$My answer:$$2x\cos \left (x^2+y^2+z^2\right )i+2y\cos \left (x^2+y^2+z^2\right )j+2z\cos \left (x^2+y^2+z^2\right )k.$$For this question, do I need to derivate $x$ for $i$, $y$ for $j$, $z$ for $k$?
2026-04-11 21:17:03.1775942223
Find a conservative vector field that has the indicated potential
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A conservative vector field is the gradient of the potential, $$ \left( {\partial f\over\partial x}, {\partial f\over\partial y}, {\partial f\over\partial z} \right) $$ so your answer is correct up to formatting issues.