(2) Find f(x) given that f"(x) = 2x + 3e". (3) Find f(0) given that f"(0) = sin 0 + cos 0, ƒ(0) = 3, f'(0) = 4. %3D (1) Find all antiderivatives of the following functions and check your work by taking derivatives: (a) p(x) = 3 sec² x Check: 2 (b) f(y) = Check: (c) f(t) = 5t(12³ – 10t) Check: 1+t+t² (d) g(t) = VE Check:

Q: find dy/do by implicit differentiation. x^3+y^3=12xy-8

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Q: 1 The derivative of the function y = cos V at z e = is equal to 4.

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Q: 1 The derivative dy for the function dx ба. [ 17 17 - ()" y : 17 dy b. [ The derivative for the…

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Q: find dy/dx of each equation using implicit differentiation. a. y4 -2y2x2 + 3x2 = 0 b. (x + y)3 =…

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Q: 1. Find dy/dx if cos 4y+ysin x =3 2. Use implicit differentiation to find the slope of the tangent…

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Q: Find the differential dy of the given function y=extanx

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Q: 7) Find dx 4e* dy if y = %3D 8) Find the first derivative of f (x) = sin? (x°).

A: We need to find out : 7)  dydx if y=4exx 8) First derivative of f(x)=sin2(x3)

Q: 1) Find dy/dx by implicit differentiation.   sin(x) + cos(y) = 7x − 4y

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Q: 1. Find the first derivative of the given function given. a. y = sint cos t b. y = 6 tan(2n + 3x)

A: In this question we have to find the first derivate of the given function.

Q: Find y' by implicit differentiation 1. x²+4x-3y²+4y=0 2. 2xy+π sin y = 2π

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Q: Find dy/dx by implicit differentiation: e^ysinx = x + xy

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Q: Explain of the method of proving the derivative (dy/dx) of y=U(x)ᵛ⁽ˣ⁾ where U(x) and V(x) are…

A: y=uxvx, where ux  &  vx are the differential functions of x. To differentiate these type of…

Q: A-The derivative is y = ln sin 0 cos 0 1+2ln 0

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Q: If sin(5x - 5y + z) = 0, use implicit differentiation to find the first partial derivatives with…

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Q: COs X Compute the mixed second order partial derivative of z =

A: The mixed second order partial derivatie of z=cos x y5  is given by ∂2z∂x∂y=5sin xy6

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: Find partial derivative of dx for the function f(x.y) given below exp 2x. siny .(at the point (In2,…

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Q: Find the derivative. y = 3t cos (t6) dt Select one: 3 A.6x cos (x ) 3 3 B.3 cos (x ) - 3^/x sin (x )…

A: The solution are next step

Q: for (e3x+y2)5 = sin x cos y, find dy/dx. using implicit differentiation. must show all steps

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Q: Get the first order derivative of the function x + sin(y – 2x) - 1= 0 - 2 1 a. y' = cos(y-2x) 1 b.…

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Q: 14. Find the second derivative of tanh xy + xy =0 by implicit differentiation. A. y" =2 B. y" =2 C.…

A: Answer is option C)  y''=2y/(x^2)

Q: Find y' by implicit differentiation. cos(x) + √y = 2

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Q: (5) Find the derivative dy/dx, where: 4 1 -1 y=- y = cosec(cot3x), y=Vsinh¯3x 3 1+ cos° x

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Find the integrating factor: cos⁡ x dy+[(y sin⁡x )-1]dx=0

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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: Take first and second derivatives of y = xr, y=(ax2 + bx + c)2, y=ecx, y=e-cx, y=ln(x).  In all…

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Q: A/ Integrate TWO only 2x dx 1) S- 2) S 4e cos4x dx 3) x In(x + x)dx x +x+1 B/ Ali is filling a cone…

A: As per the guidelines we can solve 2 problems

Q: 2. Find using implicit differentiation. Enclose final answers. dx (a) 4x³y² + x¹y³ = x + y = 0 (b) x…

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Q: valuate f¹² Vsin x + 1 cos x dx.

A: Topic:- application of integration

Q: Find dy/dx using appropriate derivative rules. 1. y = 8x^5/2 - 7x-9 + square root of 5 2. ) y =…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

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: Let y=(x to the 2nd power +3) to the 2nd power . Find the differential dy when x=4 and dx=0.2…

A: Given,    y=(x2+3)2

Q: Q /Choose the appropriate derivative for this function y = (x+ 1)2* dy = 2* (x + 1)2" - In(x + 1) dx…

A: Explanation of the answer is as follows

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: Explain of the method of proving the derivative (dy/dx) of y= U(x)V(x) where U(x)and V(x) are…

A: We have to explain of the method of proving the derivative dydx of y= U(x)V(x) where U(x)and V(x)…

Q: Suppose x and y are variable (y is a function of x) that satisfy the equation sin(x+y) =xy. What is…

A: We have to find derivative

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: Solve for the derivative of the given implicit functions. a. Find dy/dx for y= ln (4x+tan-1(lnx)).…

A: Solve: a. Find dy/dx for y= ln (4x+tan-1(lnx)). b. Find dy/dx for y= tan-1 (3x-2 sinx). c. Find the…

Q: Find the derivatives of the f: 1. y: sin (x²+3) 6. y= e tan 3x 7. y: e 2. y= tan (4x*) cot (3x-8) 3.…

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Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

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Q: Find  dy dx by implicit differentiation for the function. x2 + 3x2y2 + y2 = 6

A: Given  x2 + 3x2y2 + y2 = 6 We have to find dydx by implicit differentiation.

Q: dy 1- Find by implicit differentiation. 2- x2 + y2 = 100. 3- x³ + y³ = 3xy². 4- x²y + 3xy³ – x = 3.…

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Q: Find the first derivative 1. y = In v4-x2 %3D 2. In(x2 + y2) + 4arctan = 5 y %3D dy x+4 3. Find , if…

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Q: Explain of the method of proving the derivative (dy/dx) of y= U(x)"(») where U(x)and V(x) are…

A: The function is, y=U(x)V(x)

Q: dy of xy +y-xy=15 using implicit differentiation. dx 3) Find dy at the point (2,3) dx Hence find

A: To find dy/dx using implicit differentiation.

Q: tan(2x + 2). Find the differential dy when x = Let y : 4 and dx 0.2 Find the differential dy when x…

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Q: 5. Find dy/dx using implicit differentiation given x²y³ + cos y = 0.

A: Definition used -  Implicit differentiation -     It is a rule by which we can find the derivative…

Q: Example2: Find the derivative of w=xy+z if x=cos t ,y=sin t &z=2t?

A: