25. Use the definition of differentiability to prove that the following function is differentiable at (0,0). You must produce functions&, and e2 with the required properties.f(x,y) =x+yWhat is the first step in proving differentiablility?OA. Show that f, (0,0) f, (0,0) =f(x.y).*B. Show that f, (0,0) and f,(0,0) exist.XC. Show that,(0,0)f(0,0)= 1.O D. Show that fy (0,0) = fy (0,0).Find f, (0,0).(0,0) =.Find fy(0,0).fy(0,0) =What is the next step?O A. Show Az = f(0 + Ax,0 + Ay) – f(a,b) = f, (0,0)Ax + fy(0,0)Ay + &1 Ax+ ɛ2Ay, where e, and e2are functions that depend only on Ax and Ay, with (E1,82)→0 as (Ax,Ay)→0.O B. Show Az = f(0 - Ax,0 - Ay) + f(a,b) = f, (0,0)Ax + fy(0,0)Ay + &1 Ax + ɛ2Ay, where &, and 82are functions that depend only on Ax and Ay, with (e,,82)→0 as (Ax,Ay)→0.OC. Show Az = f(0- Ax,0 - Ay)- f(a,b) = -f(0,0)Ax-f,(0,0)Ay-e, Ax- 82Ay, where ɛ and82 are functions that depend only on Ax and Ay, with (81,82)→0 as (Ax,Ay)→0.O D. Show Az = f(0+ Ax,0 + Ay)- f(a,b) = fy (0,0)Ax-fy(0,0)Ay-(8,4x + 82Ay), where ɛ, and ɛ2are functions that depend only on Ax and Ay, with (E1,82)→0 as (Ax,Ay)→0.Evaluate the middle expression from the equation in the previous step.Az =Find the right-most expression found for Az. Choose the correct answer below.O A. Az = - Ax-Ay-eAx- E2AyO B. Az=Ax+ Ay+81 Ax + €2AyOC. Az=e,Ax+ €2AyO D. Az= -&,Ax-82AyO E. Az = Ax-Ay-8, Ax-82AySet the two resulting equations equal to each other to find &, and e2. Select all that apply.O A. e, = Ay and e2 = 0B. e, =0 and e2 = Ax

Name: 25. Use the definition of differentiability to prove that the followi
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Description: 25. Use the definition of differentiability to prove that the following function is differentiable at (0,0). You must produce functions&, and e2 with the required properties.f(x,y) =x+yWhat is the first step in proving differentiablility?OA. Show th