4. Find all second order derivatives for the following functions. (a) f(x, y) = 2x2 + 3xy + 2y?, (b) f(x, y) = sin (x – 2y). %3D

Q: 9. The anti-derivative of the function f(x) = e² + cost is (a) e²+ sinx+c (b) e² - tanz+c 10. 0.5(x…

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Q: b) Find the derivatives of the following functions: (i) 3x+4 y = tan x+5 (ii) y = e* -cos3x + x log.…

A: Derivatives

Q: Can you help me with this problem step by step?

A: Given:

Q: 1.2 s Find first derivative for the following functions. dx (a) y = 5+ 6x + 4x3 (b) y = In(2x) +x*…

A: Note:-Since you have asked multiple questions, we will solve the first question with three sub-parts…

Q: - 9x Find the derivative of y with respect to x if y = e dy %3D dx

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Q: Given sin(x?y²) + y³ = x + y , using implicit differentiation for partial derivative show dy that dx…

A: Implicit derivative dydx of sinx2y2+y3=x+y

Q: 4 the second order For the function y = 4 e" - - d'y is derivative dx? 4e + 8x-3 O 4e" + 4x-2 -3 O…

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Q: 1. Find the derivative d/dx using implicit differentiation of the following functions. Show your…

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Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x³–2x)* 1. у- ; d'y/dx? 2. Y = (5x³ + 2)6…

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Q: Ift=2cos (y² + 2), find the derivative of t with respect to y. A. 8y sin(y² + 2) cos(y² + 2) B. –8y…

A: The given function,  t=2cos2y2+2

Q: 11. Find the first derivative of y = arccot (). a. y' 1+ b. y' = 1+x² 21 c y' = 14 d. y' = 14x0 e.…

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Q: Given that y is a function of x defined implicitly by the equation: siny = 4x + xy dy Find the first…

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Q: 51. The functions y = e* and y = x³e do not have elementary anti- derivatives, but y = (1 + 3x)e"…

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Q: 1. Find the y" of y = (4x - 3x + 1) (5x + 7) 2. Find y" given y = cosx + sin 3x 3. Find all the…

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Q: 1. Find the derivatives of the given functions. a. y= arccos(x b. y = In (arctan x) c. y= csc (2u+1)…

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Q: 5. What is the derivative of the given function below? * x² + y² = xy dy dy dx dx Option, dy dx = =…

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Q: Calculate the first numerical derivative of the following equation with the values xo = 1 and y o =…

A: Given function is fx,y=ex3y−sinx,  x0=1 and y0=15.6 for Δx=Δy=0.1 We have to find the first…

Q: 4) a) Determine the derivative dx of the following functions y = 3** b) 1-3- 3e² 1² c) y d) y =…

A: We have to find the derivative.

Q: 4. Find all second order derivatives for the following functions. (a) f(x,y) = 2² + 3ry +2y², (b)…

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Q: 2. Find the derivative (dy/dx) of the following functions: h) y = 3x7 - 7x3 + 21x2 i) y = (x2 +…

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Q: Find the derivative of y with respect to x. y = sin (e 5t) e 5t e OA. 1- e 10t 5e 5t O B. 1- e 10t 5…

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Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d.…

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

Q: Can you help me step by step?

A: To determine the value of first and second derivative of the function

Q: Q2 find the derivative of the following: 1) y = 2sin?(5x) ,2) y = lnx'ncosh 5x ,3) xsin-14y = y…

A: See the attachment

Q: Q. No. 5. Find the Derivative of the Given fur a) y= ev1n x( Inx) +2x b) f(x) = %3D a+x

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Q: Find the differential dz of the function f(x, y) = 4y² + x²y-2xy and use it to approximate Az at…

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Q: What is the derivative y^2 = 64 with respect to t? O 2x dx/dt + 2y dy/dt = 0 O 2x dx/dt + 2y dy/dt =…

A: Given that,  x2+y2=64

Q: Q-1: find the derivative of y with respect to the given indepe 1. y = In(Inx) 2. y = In(In(Inx)) x…

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Q: Suppose that x and y are related by the given equation and use implicit differentiation to determine…

A: →duvdx = udvdx + vdudx→dkdx = 0  where, 'k' is any constant.

Q: Find the derivative of y = x°e*. O a. y' = 3e*x2(e*+x) O b. y 3x2(e* +1) O c. y = e*x2(x+ 3) O d. y'…

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Q: Q1)Find dy/dx for the implicitly defined relation sin(xy^2)=xarctan(y). Q2) Find the first two…

A: Given:sin(xy2)=xarctan(y)Differentiate both sides:cos(xy2)y2+2xyddx(y)=arctan(y)+xddx(y)y2+1Isolate…

Q: 4. For the given derivative, find the antiderivative that satisfies the indicated condition. f '(x)…

A: We have to find the anti derivative of the function or we can say that we have to integrate the…

Q: Find the derivative of y with respect to t at t=2 if a) y = cos (x) – cos(1+x²) and x = [sin(t – 2)…

A: The derivative of y with respect to t is:

Q: 4. Find the indicated higher-order derivative of the given functions. d'y а. у %3D 8е* + sin x; dx7…

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Q: (c) Find dy/dx by implicit differentiation cos(x² y) = x

A: We are given, cos(x2y) = x We need to find dy/dx

Q: Calculate the derivatives of the following functions.(a) y= 4x2 + 4(b) y = sin 3x+ 4 cos 2x(c) y =3x…

A: We have to find derivative of the given function. (a). dydx=d4x2+4dx=8x   b.…

Q: 14. Find the derivative of y = e cosz %3D A. y' = -ecosx sin z B. y' = elinx cos x C. y' = -etinx…

A: Given,y=ecosxdifferentiating both the sides w.r.t. xdydx=ddxecosxUsing chain…

Q: Find the derivative of y: 1- y = (cos 0)▼2

A: See the details solution in below

Q: 1. Find the respect y = 2x5-x² 3x - 20 derivatives with to X using dy using o 12-1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: 4. a) Find the following derivatives using differentiation rules. d dx 5 2)* d ii) Vx + dx d²y b) If…

A: 4 First we will see differentiation rules.…

Q: 14. Consider the curve defined by x2y2 - 3x2 - 6y2 0. dy a. Use implicit differentiation to find :…

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Q: 3.9.27 Find the derivative of y with respect to x. y = sec 1(5x2 + 1). -1(5x2 +1), x > 0 dy %3D dx…

A: Please see the answer in Step 2

Q: (2) Find the derivative of the following: In xy = e*+y 4. %3D y = esint (In t² + 1) 5. y = In e 1+e…

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Q: - 18x Find the derivative of y with respect to x if y = e dy %3D dx

A: We have to find the derivative

Q: Find the derivative of y with respect to x. y = tan -1V3x O A. V1- 3x 1 O B. 2(1 + 3x)/3x 3 Oc.…

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Q: Can you help me with this problem step by step?

A: Differentiating implicitly with respect to x on both sides. Solving left hand side first.

Q: Find the differential dy of the given function. y = √(9 − x2)

A: The given function is Now, find the derivative of the function

Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: (1) Suppose that y is a function of r satisfying the equation 5x + 10y + 3.ry+ 5y + 6x 0. Use the…

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