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ENG1005 - MUM S2 2025 [FINAL REVISION] Quizzes

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Question textLet [math: f(x,y)=ysin⁡(xy)]f(x,y) = {y\,\sin \left( x\,y \right)}. The partial derivative [math: ∂f∂y]\frac{\partial f}{\partial {y}} is[input] Your answer should contain the variables [math: x] and [math: y].Check Question 66

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The function given is f(x, y) = y sin(xy). To differentiate with respect to y, we use the product rule since f is a product of y and sin(x......Login to view full explanation

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Question at position 1 If f(x,y,z)=x2yz2+xy2z+xyf\left(x,y,z\right)=x^2yz^2+xy^2z+xy, then fx(1, 2, 3) =36.none of the above55.50.48.

Question text 6Marks Consider the function [math: f(x,y)=x2y2+yex−1.] f(x,y) = x^2y^2 +y e^{x-1} . a) Calculate the following partial derivatives at the point [math: (1,1)]: [math: ∂f∂x=]\frac{\partial f}{\partial x}= Answer 1[input] [math: ∂f∂y=]\frac{\partial f}{\partial y}= Answer 2[input] [math: ∂2f∂x2=]\frac{\partial^2 f}{\partial x^2}= Answer 3[input] [math: ∂2f∂x∂y=]\frac{\partial^2 f}{\partial x\partial y}= Answer 4[input] [math: ∂2f∂y2=]\frac{\partial^2 f}{\partial y^2}= Answer 5[input] b) A tangent vector to the level set of [math: f] at [math: (1,1)] is [math: (1,] Answer 6[input][math: )].Notes Report question issue Question 5 Notes

Question textLet [math: f(x,y)=ey+x2]f(x,y)={e^{y+x^2}}. What is [math: ∂f∂x(0,0)+∂f∂y(0,0)]\frac{\partial f}{\partial x}(0,0) + \frac{\partial f}{\partial y}(0,0), the value of [math: ∂f∂x+∂f∂y]\frac{\partial f}{\partial x} + \frac{\partial f}{\partial y} at the point [math: (0,0)] ?[input] Check Question 67

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