Determine whether the vector field is conservative, and, if so, find a potential function.F =(cos(z))i +(20y)j (x sin(z))kStep 1 of 4Recall the cross-partial property of conservative vector fields.F =P, Q, Ris conservative if and only ifPy = Qx, Qz = Ry, and Pz = RxUse this property to check ifF =cos(z),20y,x sin(z)is conservative.Py=$$0Qx=$$0Qz=$$0Ry=$$0Pz=$$sin(z)Rx=$$sin(z)ThusF =cos(z),20y,x sin(z)isisconservative.Step 2 of 4We wish to find a potential function,f(x, y, z),such thatF =f.Thuscos(z)= P = fx.Integratefx = cos(z)with respect to x, holding y and z fixed.f(x, y, z)=cos(z) dx=xcos(z)+ h(y, z)We need to determineh(y, z).To do so, differentiate this expression with respect to y.fy =+ hy(y, z)