Q3|A: Find ý if 1-y = cot vx +2 2- y = tan v+ Vtan x 3- y = tan x+ * cot v

Q: 2. If f(x, y)=x² sin y-y cos.x-xe - ye" +5x°y°, show that ô²f _ ô²ƒ ôxôy ôyôx

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Q: 3. Find , 9 for the functions: ax' ây sin(x³ + y* ) x* +y , (x,y) = (0,0) f (x.y) = .(x.y) = (0,0)

A: f(x,y)=sinx3+y3x2+y2, x,y≠(0,0)0, (x,y)=(0,0)

Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

Q: sin, ifx T 2л

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Q: 2. If f(x, y)=x² cos y-y' sin x-xe'-ye* +2x*y', show that ôxôy ôyôx

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Q: dy/dx= tan^2 (x) / sec^2 (y), y=pie/4 when x=0

A: given,                 dydx=tan2xsec2y and           y   = π4 when x =0

Q: a) f(x) = 3x + 5; interval [1,2]; %3D W = 10 interval ; 11m- b) f(x) = sin x;` %3D W = -1 2' 2

A: To verify the IVT for the specified function f, the interval a, b, and the indicated value w.a…

Q: af Find of f (4.v) = sin ) 1+ y

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Q: 2 1 + x - 1 then find dy when – 1<x <1. If y = tan dx

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Q: b) f(x) = cosx on the interval [0,] %3D

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Q: If f (x) = A (В B C D Stams. 0 sec²x tanx 1+1² Ite¹ 1+e tanx sec ³x 1+e -dt, then f'(x) equals tanx…

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Q: find ∂z/∂x   sin(yz) = z − x

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Q: Suppose f(x) = 3*sec(3*) tan( 3*). Evaluate: / s(x)dx sec(3*) A +C In (3) 3*. sec(3*) +C B In (3) ©…

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Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: 2.xy x² – y? Show that - = 0 if z= Tan

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Q: Find if f(x,y) = y sin xy ax %3D az Find ax if yz – In z 4. = x + y 3.

A: Given that: f(x,y)=y.sin(xy)   NOTE: As per our answering guidelines, we can only answer 1 question…

Q: 2 = using the relation r= VT show that sin x %3D EX II

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Q: Find domain and vange f (2y)- し、 (x'+ゴ) ) fCz, y) = Sin" (y-z) Ž (3,y)- tan

A: According to the question,  We need to specify the domain and range of the given function: (A) f(x,…

Q: (b) If f (x, y) = y sin2x + x°cosy °cosy 3 then verify dxðy dyðx

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Q: tan x If h(x) Vt + vt dt, then find ht(x). 0,

A: We apply here Leibniz rule

Q: 2. Find if y = esinvx dx A. (sin vx)esin vã-1 cos vx В. (esin væ) 2 vx e Cos vã С. 2 vx (cos Vx)esin…

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Q: Hw) if J-0- Gso and X=O+ Cas e Show that Sece+tan 0

A: The given differentiation can be solved by using chain rule. Initially, the y expression can be…

Q: d sec z = sec z tan z dz

A: The function is a rule that associates or fixes a number to the particular point z . If , then the…

Q: 4) If F(x)= } d, then F'(x)- sin t

A: Note : According To our guidelines we can solve only first question and rest can be reposted.Thank…

Q: (3) Let f(x, y) = 3+sin(x) 4y2+10 Find both fa(r, y) and fy(x, y).

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Q: If f(x) = (A) B - St √1+1² 1+e' 0 In (secx) √ 1+tan²x tanx 1+e 1+tan²x tanx D tanx 1+e sec ³x 1+…

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Q: b). Determine if y =x tan (x) satisfy dy_y x sec²(x) = 0 when y|x=0 = ( | dx

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Q: 1. Find the most general f(r, y) obeying öróy - sin(x)y.

A: As per guideline we can solve only one question you can repost other questions in next question

Q: Find the -of the following function : ду w = cos (x2 + 2 y) – e4x- z*y + y3 .A a w = 2 sin ( x2 + 2…

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Q: If sin(x) F(x)= V2+t2 dt /tan(x) and g(y)= dx . g" (4) Then is equal to V5 - 2 V3 2 V3 2 - 2 V3 V –…

A: Given :  fx=∫tanxsinx2+t2dt Differentiating both sides Using Leibnitz Rule, we get…

Q: rez If F(x) = -7 sin t dt, then F'(x) =| %3D In x

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Q: : (a) Evaluate S cosx sinx V1 – sin+x_dx. (b) Evaluate S V1 – x² dx.

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Q: 1 -dx= cosº x/2sinx 5 /tanx+=Vtanº x + C А. Vtanx+/tan5x+C 1 B. tanx +÷Vtan° x +C С. 2 2 tan x +C 1…

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Q: (f) y = e* In(tanh(x))

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Q: on) b) Find if tan²y = x² + o V²+1 dt %3! dx Jysinx

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Q: The value that will satisfy potentia. function p is x + y sin x None = In (x +y %3D

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: d tan(2) = %3D dz sec(x) O cot(x) O sec-(z) O sec (z) tan (z) O

A: We use the standard results of derivatives.

Q: a) Use the definitlon of derlvative to find ds If dt 2t+1

A: As per bartleby guideline for more than one question asked only first is to be answered please…

Q: Q6:-Prove that: y" = 1 y =csc(tan"" ) if

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Q: Determine the interval in which solutions are sure to exist. y" + ty" + ty' + t'y = ln(t) Valid on…

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Q: Find f-(x, y) and fy(x, y). f(1, y) = (y^tan(4x)) fa(x, y) : fo(x, y)

A: The given function is: f(x,y)=y5 tan(4x)-43

Q: Hei! If y cos(xy) dydx = x=0 y=0

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Q: If f(x) = f = Stanu √I+1² 0 1+e' In (secx)√1+tan²x (A) tanx 1+e sec ³x В) Ⓒ (D) tanx 1+tan²x 1+e…

A: Application of integration

Q: 9. If f(x,y) = -cos x+e*y, find Vf(x, y).

A: For the solution follow the next step.

Q: If f(x) = (A) B C D tanx sec ³x 1+e 1+1² 0 sec²x 1+ e tanx In (secx)√√ 1+tan²x tanx 1+e 1+tan²x 1+ e…

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Q: If f(x)= (A) B D plans √ 1+1² tanx I+e' f sec ³x tanx 1+tan²x Itefan 1+e -dt, then f'(x) equals…

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