20. For the function z = f(x,y) = x? – y + 2, write a formula to calculate approximately the change in z, dz, determined by the small changes dx and dy about the point (1,1).

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

A: topic - derivative of a function

Q: The differential of y = (5x-6)e2z has the form | dy = (mx + b)e2# dz %3D Find the values of m and b.…

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Q: If x? + y2 = 100 and dy/dt = 9, find dx/dt when y = 8. (Enter your answers as a comma-separated…

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Q: Let y tan(4x + 4). Find the differential dy when x = 1 and da 0.4 Find the differential dy when a =…

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. −x2+3x−5=2y2 −2y

A: We have to find derivative (implicitly ) with respect to x .Curve equation is given by:

Q: Assume that x and y are both differentiable functions of t and are related by the equation…

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Q: Find the differential dx for the function: y=V4+5x at x 0 and dx 0.04. 0 5 O 0.08 O 0.05 O 0.8

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Q: How would you verify that the following equation is not exact?(-xysin(x)+2ycos(x))dx + 2xcos(x)dy =…

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Q: Find dy/dx and d^2y/dx^2 X=t-e^t, y= t+e^-t For which values of t. Is the curve concave upward?

A: Given that, x=t-e^t, y= t+e^-t

Q: find dy/dx for the function ex+y+2x-3y=e using implicit differentation.

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Q: Q1-lf x= cot-VE, y= , find dy dx' dx2 at t = 2. t+1

A: We have to find first order and second order derivative of the given parametric functions.

Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

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Q: ²+ re" = 2y + e² %3D

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Q: Find the value(s) of dy/dx  at y=1 given that x2y + y2 = 5.

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Q: - 16y? – 16x – 16y = 0. dy at the point (3, dx ves to calculate

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Q: (1) Use the Chain Rule to find dz/dt. (a) z = r² + y² + xy, r= sint, y = e'. z = x2 +y?, x = cost+…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: (b) Given that y(6x +1) e** = 1+ - In dy Find when x 0 and y=1. dx

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Q: 5. Calculate the following derivative x = 3e d y %3D Find (1) y=2e [y= 2e' ; dx? %3D dy 2) Let the…

A: (1) Given x=3e-t  and   y=2et The objective is to find d2ydx2. Now, dxdt=-3e-t and dydt=2et Then…

Q: Find  dy dx at the value of the parameter. x =    t,  y = 2t + 8,  t = 16

A: See attached file for a step by step explanation.

Q: dw by using Chain Rule. (Your answer should not include z ond y. dt = z+v? z = cost + sin t and y=…

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Q: Find the differential dy of the given function. (Use "dx" for d> y = 8x² – 4 dy = %3D

A: Formula :

Q: Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dy dx…

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Q: If the new DE is written in the form M(x, y) dx + N(x, y) dy = 0, one has My = || N, = X, Since M,…

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Q: 2. From the following table of values of x and y, obtain equation for dy/dx and d'y/dx? and its…

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Q: Find dy/dx for the following functions:- (2) y = v sinh Vtan x (4) y=2,u = 3x²-2 u²+1

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Q: where t is a non-zero parameter. Show that dx 28 Given that x=z and y==. 1+r Hence find its value at…

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Q: Let y = tan(3r + 4). Find the differential dy when T = 4 and da 0.4 Find the differential dy when x…

A: Given: Differentiate the above expression of 'y' with respect to 'x'.

Q: Find the length of the curve y = ln sin x from t = −2 to t = 0.

A: f(x)=y=ln(sinx) Arc length =∫ab1+(f'(x))2dx f'(x)=dln(sinx)dx=1sinxdsinxdx=cosxsinx=cotx a=-2 b=0

Q: Let y = f(x), where f(x) = 3x+6/x+6 Find the differential of the function. dy =?

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Q: В. Find dz/dx , əz/@y at the point (1,1,1) if x³ + z2 + ye*z + xz cos y = 0 .

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Q: Obtain dy from the following function y= e v*

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Q: i) Find the length L of the curve y = x + cos x, 0<x <T/2 Use any one of the following formulas 2…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) x + 1 5x − 7 dy = | y = X

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Q: Given a = 2 cost+35 and y =7sin t %3D dx dt dy dt |3|

A: Topic : differentiation

Q: 22. Find when t=, where x a(t + sint), y= a(I-cost) and a is a constant %3D

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Q: Let y = (x + 3). %3D Find the differential dy when z = 2 and dz = 0.2 Find the differential dy when…

A: Given:  y=(x2+3)5  Differentating y with respect to xdydx=ddx(x2+3)5Using differential power rule…

Q: (i) Find the linear approximation of the function f(x, y) = 1 - xy cos πy at (1, 1) and use it to…

A: Here, the given function is: f(x,y)=1-xycos πy To find the linear approximation of the function. For…

Q: Find the differential dy of the given function. (Use "dx" for dx.) 8 y = 2√x + 4 dx *- (√x +++1)x dy…

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

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Q: Show that the equation dy/dx=x^2/(1−y^2) is separable, and then find an equation for its integral…

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Q: 4. An earth satellite moves in a path that can be described by x2 72.5 = 1 71.5 where x and y are in…

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Q: Let y tan(3x + 6). Find the differential dy vwhen a 2 and da 0.4 Find the differential dy when z 2…

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Q: Find the value(s) of dx at y= 1 given that x²y+y² = 5. only В only 2

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Q: Find the differential of the function. y = V 3 - t 35 dy = V 6 3 –

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Q: dy Find dx for implicit function ete + 3 x° cos y + 3y² = e4* + 3

A: Given that: x3.cosy+3y2=e4x+3

Q: Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

A: We have to prove 4y*f'x - x*f'y = 0 Also calculate g'(t).

Q: If x2 + y2 = 100 and dy/dt = 4, find dx/dt when y = 6. (Enter your answers as a comma-separated…

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Q: dw b) If w = (x + tanx). (Vx – 1), and x = tan (cost) find dt

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