– x®y³, 6. Given f(x, y) = e®° - show that fxy = fyx.

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: 2 consider, Differentiate with respect to x', dy C」.2ス %3D de

A: From the image , two find a differential equation eliminating the constants from the given relation.…

Q: On what interval is the curve t2 X. dt y% = Jo t2 + t +2 concave downward?

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Q: Consider w = x² – y², where x = s cost and y = ssin t. Find u and hu using the Cha dw at ds Rule.

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Q: A) Use the chain rule to find where w'sy',x= sint + cost y = cost - sint. B) If f(x. y) - xy?+ x'y ,…

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Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: Q2/ by using chain Rule to find dw at t = 1 if dt w = 2ye* – Inz ,x = In(t? + 1), y = tan 1t,z = et

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Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: Given f(z) = | t2 – 16 dt 1+ cos²(t) OS At what value of a does the local max of f(x) occur?

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Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: Express in form y=f(x) by eleminating the parameter x = t , y = tan−1(t3 + et )

A: It is given that,

Q: Use the attached equation to find  dy/dx for this: 5tan−1(x2y) = x + xy2

A: Given, 5tan−1(x2y) = x + xy2

Q: Given z = 18 In(t) and y = 324 t2 then find dy dz dy da?

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Q: What is P,(y) if the given DE is xydx – (3y – x²)dy = 0? %3D Select the correct response:

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Q: S. Find f(t), if f'(t) = df 1+ cos(2t) and f =1. %3D %3D dt

A: To find the function f(t) following the given conditions.

Q: (Xy,Z)%3Dex(cosy +sinz) fr?, fy =?

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Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: COS. dt, for alla at, for all r 58 1 dt 58. for |x| < 1 (1 – t4

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Q: Show that the function y(x, dy/at = a2y/ar2 = dy/ax = %3D %3!

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 3. Given f(x,y) = xy + y2 +1° ey Verify that fry = fyx %3D

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Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

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Q: Without eliminating the parameter, find d²y at t = 2 1 x = 1

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Q: If y= Vx (x-1), find dy (Use rules, not a XP de finition

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Q: Q10. Expand f (x, y) = e" cosx about up to third degree terms by using Taylor's theorem for a…

A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

Q: Hw z] Find Sxsin(x)dx using this rule.

A: Given that, Using the chain rule, The integral becomes,

Q: Given f(x, y, z) = xe"y + sin(xyz), find fyzz

A: Derivatives of: Sin x is Cos x Cos x is -Sin x u

Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

Q: Q3) for f(t) = sec?(6t – 1) and g(t) = tan?(6t - 1) show that %3D f'(t) = g'(t).

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Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: The approximation of x'e"dx by Gaussian Quadrature with n=2 is (Use c21 = C22 =1 and r21= r22

A: Given :                 I = ∫01xeexdx

Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: If u- f(x) where y=J x+y%*34 show thal do

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Q: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

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Q: A volleyball is moving 16 m/s at 25o North of straight down. If +x is East, +y is North, and +z is…

A: Draw the sketch, as follows: Since the ball is moving 25° North of "Straight Down" direction, its…

Q: Q3) for f(t) = sec²(6t – 1) and g(t) = tan?(6t – 1) show that %3D %3D f'(t) = g'(t). %3D

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Q: Given f(z, y) = 7x° cos (y*), find fzy(z, y) = | fyy(T, y) = [

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Q: Suppose that f(x, y) = e 42? - ly + 7z + 2y then find the discriminant of f.

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Q: Given f(x,y) = ex cos y, Evaluate fy(2,0) O e² cos 2

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Q: What is the I.F of dy/dx=(y+y^2)/x?

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Q: If y= V (x-1), find dy (Use rules, not a de finition ) Xp

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Q: Show that the function u = 9(ry) + /TY v(y/x) provides the uation ‚²u y? 0. dy?

A: First find the partial derivative of the given function with  respect to x :

Q: Find the directional derivative of Du f(2,1) in the direction of: d = 7i + 2j To f(x, y) = In(Ges…

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

Q: Find dwdt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: The function w=xycosz, x=t,y=t2,c=arccost. Then we have to find dwdt(a) by using the appropriate…

Q: Given f(x, y) = - (4x°y + xy® ). Compute: dy?

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Q: If z'y +y = r dy 1, then at (0,-1) is

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: what is (x fyx+ fy) given fCKiy)= ey

A:

Q: Express in form y=f(x) by eleminating the parameter x = e−2t , y = 6e4t

A: Here, x=e-2t and y=6e4t

Q: Q5.a) Find if sec?y = x² + S t² dt Jsiny

A: P.S.: please ask one question at a time.

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: