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多项填空题

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Question textCompute the following partial derivatives of [math: 2xsin⁡(y+x)+1]. In your answers Be sure to double check you include all multiplication symbols! Double check the "The variables found in your answer were:" box to be sure it ONLY has x and y. If it has, say, xe as well then you have forgotten a multiplication symbol. [math: ∂f∂x=] [input] [math: ∂f∂y=] [input] [math: ∂2f∂x∂y=] [input] [math: ∂2f∂y∂x=] [input] Your last answer was interpreted as follows: -2*x*sin(x + y)+2*cosThis answer is invalid. Forbidden variable or constant: cos. Check Question 1

Question textCompute the following partial derivatives of [math: 2xsin⁡(y+x)+1]. In your answers Be sure to double check you include all multiplication symbols! Double check the "The variables found in your answer were:" box to be sure it ONLY has x and y. If it has, say, xe as well then you have forgotten a multiplication symbol. [math: ∂f∂x=] [input] [math: ∂f∂y=] [input] [math: ∂2f∂x∂y=] [input] [math: ∂2f∂y∂x=] [input] Check Question 1

Let the production function be 𝑌 = 𝐾 𝛿 𝐿 1 − 𝛿 and 𝛿 = 0.4 . Moreover, 𝐾 = 1200 , 𝐿 = 245 . Then the ratio MPL APL = ______. (Recall, M P L = ∂ 𝑌 ∂ 𝐿 and A P L = 𝑌 𝐿 .) Round your answer to the nearest hundredth.

Question at position 2 If z=yx2+6yz=y\sqrt{x^2+6y}, then ∂z∂y=\frac{\partial z}{\partial y\:}= yx2+6y+x2+6y\frac{y}{\sqrt{x^2+6y}}+\sqrt{x^2+6y}3yx2+6y\frac{3y}{\sqrt{x^2+6y}}3yx2+6y+x2+6y\frac{3y}{\sqrt{x^2+6y}}+\sqrt{x^2+6y}(2x+6)yx2+6y\left(2x+6\right)y\sqrt{x^2+6y}x2+6y\sqrt{x^2+6y}

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