5. Calculate the following derivative x = 3e d y %3D Find (1) y=2e [y= 2e' ; dx? %3D dy 2) Let the function y = f (x) be determined by the equation y =1+xe' find dx |(0,1)

Q: dy 5. Use Implicit Differentiation to find dx a) 4xy + x² = 4 - Iny³

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Q: 1 5 X If y = - find dy dx at x = 2.

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Q: 14. Determine dy/dx if y is a function of x defined implicitly by sin(x? + 2y)

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Q: Find the second derivative d2y/dx2 of the implicit curve y3=xy+1  at (0,1)

A: y3 = xy +1differentiating both wrt to x3y2dydx= y+xdydx+0dydx3y2=ydydx= y3y2-x

Q: x² S cos(VE) dt dx 'x

A: Given ddx∫xx2costdt

Q: dy Find the derivative of the function æ' In 3y = y sin 3x + e. %3D

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Q: 2. Consider y = cos(2x). 2.1. Find Y dx 2.2. Determine an equation for the tangent line at x 0.

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Q: 2(y+1) dy t 2) 2(у + 1)4 dx x+1

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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: OFind the second derivative of y = 4Vx + E + 10

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Q: Find the derivative of y with respect to x for y = sinh 1(11/15x). dy 165 dx 2/1815x? + 15x

A: Given query is to find the derivative of the expression.

Q: In (3x) Find the derivative of y with respect to x if y= sin (7 e') dt. dy dx

A: Given : A function is given as: y=∫0ln3xsin7etdt To find : The derivative of the function y.…

Q: find the derivative (dy/dx) of the given function:  1. y= e^X sin X 2. y= (cos x)^9 3. 1/ ln(X)  4.…

A: Given,

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: 10. Find the derivative of y = ln 4**+1) In 4 dy A) dx 2x dy 2x In 4 B) dx dy 2xIn 4 C) dx 4(*+1) dy…

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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: 9. Find dy/dx by implicit differentiation of y? = In(x), at (e36,6).

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Q: Derive the formula dy 1 dx 1 + x? for the derivative of y = tanx by differentiating both sides of…

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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: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 2 1. Z= 1+x? ; d²z/dx? 2. Y = (3x + 2)* ;y"…

A: Given function is: y=3x3+24 We have to calculate d2ydx2 or y''. Now we see,…

Q: 2. Evaluate dy and Ay if x = 1 and dx = Ax = 1. 3. Find the equation of the tangent line at x = 1.

A: Your question contain only two which i have solved completely.

Q: 4 For the function y = 1 e - dy the second order derivative dx? is

A: Given that a function and find second derivative of this function (d2y/dx2). We know that d(xn)/dx =…

Q: Find dy/dx for y = 3l(sin-(e-3**)12 dy 3(sin"(e-*)* In3 2(sin-"(e-3x*)- dx 1(-6х) V1-e-6x2

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Q: 1. Find the centered difference approximations of 0(h^4 ) for the first derivative of y=sin(x) +…

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

Q: Find the derivative of y with respect to s. y = sec 1 (5s° + 2) dy ds

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Q: 1) In this problem, let * = 2, the value Ar = dx, dy = f ' (x)dx, and Ay = f(x + Ax) - f(x) to…

A: According to the guidelines issued by the company We are supposed to answer only one question.…

Q: Take the derivative of the following: Dy= 3xe y = e (3) e y = @y= In () 10 Y=ln (In x)

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Q: 19. What is the derivative, of the function, dx dy y = 3x2 + 6x – 4 + 2e* – 3ln x А. dy 3 32x + 6 –…

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Q: 1. Find the derivative of the following functions (dy/dx) at x=Tt/4 cos x2 1– sin x2 y= 2. Find the…

A: We have to find the derivatives of given function at x=π/4  1. y= cosx2/(1-sinx2) 2. y=x3sin3xcos3x

Q: Whatis the derivative of y = sin (2x − 1)? dx = 2 cos (2x - 1) dy dx = cos 2x dy -2 cos (2x - 1) cos…

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Q: 1. 2x'y² + 4yx² = 6. Find dy/dx at (1, 1) by i- %3D

A: Here we have, 2x3y2+4yx2=6 ................... (1)  Differentiate with respect to x

Q: 2. Please find the derivative of the following: S* cos vt dt J. cos b. Scos VE dt a.

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Q: 6. Let y + xy - y = 8x*. a) Find dy/dx using implicit differentiation. b) Find the equation of the…

A: In implicit differentiation, when we differentiate y, we use dy/dx

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

A: Given:

Q: 1. Calculate the derivative of the following function. y= V2x + 19 dx 2. Calculate the derivative of…

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Q: 3. Find dy/dx x = Vy + Vỹ 1 + Vx 4. Find the second and third derivative of y = 5. Find dy/dx y =…

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Q: 2. : Consider the function ry + cos y + x 2+ xy. (a) Find the derivative, dy/dx. (b) Find the…

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Q: Can i get help step by step?

A: We take ln on both sides and use logarithmic differentiation. Using the product rule and power rule…

Q: i. y = cosh(2x – 1) %3D 1 j. y = arccosh H| 8

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Q: 9. Find dy/dx using implicit differentiation, °y- xy = 4 |

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Q: 2- find dy/dx e2x = sin (x + 4y) 3-find an equation for the line tangent to the graph f(x) = x –…

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Q: 4 Suppose that r + y* = 82. dy (1) Use the method of implicit differentiation to find da dy dx (2)…

A: Please see the answer below.

Q: In (3x) Find the derivative of y with respect to x if y = sin (7 e') dt. %3D dy dx

A: Given y=∫0ln3xsin7etdt.We need to find dydx

Q: Compute the second derivative of e^x+y+y^2+x^3=0. y" denotes, d^2y/dx^2

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Q: 1. Find the derivative of the following functions (dy/dx) at x=0 y= sin 2x – 2sec x 2. Find the…

A: We are given: y=sin 2x - 2 sec x and y = sin4 4x - cos4 4x We need to find their derivatives at…

Q: 4- Find dy/dx for y = 3(sin-(e-3x*)2 dy 31(sin-(e-3*")r* In3 2(sin-'(e-3x")- dx 1(-6х) е 1 - e-6x2

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Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

A: