Given that f(x) = x°h(x) h( – 1) = 3 h'(- 1) = 6

Q: Find the value of the derivative y′(x) at x=0 for the function given by ey+xy=e.

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Q: 2. Obtain the general solution to the equation dy dx x sin x y cos y

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Q: x² S cos(VE) dt dx 'x

A: Given ddx∫xx2costdt

Q: 18. y = x/I - x?

A: Differentiation:- The derivative of a function of real variable measures the sensitivity to change…

Q: Find the differential dy of the given function y = √(36 − x2)

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Q: Find the differential d5y of the function y=sin2x.

A: To Determine: Find the 5th differential of the given function y = sin(2x)

Q: Given that the first derivative of x^81+y^81=-36 is given by dy/dx=kx^c/y^c,what is the value of k?

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Q: the implicit derivative of     sin(y) − xy^3 = e^(−3x^2)

A: Givensiny−xy3=e−3x2

Q: Given: x3 + y3 - 3xy 0, solve for dy by implicit differentiation. %3D dx

A: The given function is  x3+y3-3xy= 0  We have to find dy/dx.

Q: Find the slope of the curve 2xy = In(e*) sin(x) at the point (2,2)

A: to find the slope differentiate  the equation with respect to x .

Q: Find the differential dy of the given function.

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Q: A particle moves along the x-axis with velocity given by v(t) = 67 sin (at) for time t> 0. If the…

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Q: Find the differential dy of the given function. y = 3x − sin2x

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Q: If y = f(x) is the solution of (-x – 9)dx + (x2 + 10x + 41)dy = 0, f(0) = }In(41) +arctan(5/4), then

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Q: 9. Sinte)e x(t² + 1)dt = x ,(t² + 1)dt S' 2* dx < S, xdx 10. dx = dx + dx 11.

A: 9.∫ln(e)0ln(e)ex(t2+1)dt=x∫0e(t2+1)dt10.∫012xdx≤∫01x dx11.∫131xdx=∫151xdx+∫531xdx

Q: Find the differential d4y of the function y=x4.

A: Given function is

Q: A particle moving along the x-axis has velocity function v(t) = t sin t. How far does the particle…

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Q: If s = f(t) denotes the position of a particle at time t, the derivative f'(c) is the of the…

A: Solution:Given      If s=f(t) denotes the position of a particle at time t, the derivative f'(c) is…

Q: 3. Determine the Particular solution of this equation In terms ofY (xy2)dx + e*dy 0, as x → 0, y ==

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = x+3/2x-3

A: Quotient rule of differentiation:

Q: A particle moves along the x-axis with velocity given by v(t) = 6T sin (2nt) for time t > 0. If the…

A: Given: vt=6πsin2πt at t = 1, x = -4

Q: 2. If y = x +3x-2x+1, find the values of the following e. derivative, i. У"(2) d'y ii. dx ii. y" (2)

A: Please refer to the image below

Q: Find the differential dy of the given function. (Use "dx" for dx.) 6. y = 2/x +

A: Given:

Q: 1. Solve for y of the Separable D.E. sinx dx +y dy = 0

A: To solve the given differential equation for y.

Q: If f(x) = x^2 sin(3x), find the differential dy

A: Consider the given: fx=x2sin3xy=x2sin3x Differentiate w.r.t. "x", dydx=ddxx2sin3xApply the Product…

Q: Find the differential dy of the given function. dy sec x x² +9

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Q: -TL 4.) x² sin(xy) dydx

A: Given ∫0π∫01x2sinxydydx

Q: Find the differential dy of the given function. y = Invs - x dy =

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Q: dy/dx of y=cos^-1 (e^-3x)

A: Given y=cos-1e-3x

Q: Find the differential dy of the given function.    y = x tan x

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Q: In integrating the function f(3x + 5)(cos ) dx using integration by parts, what would be your du?

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Q: Find the differential dy of the given function. y = √x +1/√x

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Q: The derivative of the function y 1 = COS Va at a = 0 is equal to

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Q: The of the function y= e sin(3x)- In(5.x +2x+1) dx at (0,0) is: А. О В. -1 С. 1 D. 3

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

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: The equation of the tangent line to the graph of f(x)=ln(x) at x=e^−1 is given by y=mx+b for m =…

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Q: Find the derivative of the function. - c() (수 1 - e9x 1 + e9x y = cos y' = 18e9z sin + e&= )…

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Q: ydx -( x+***ty? dy = 0

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Q: Find the differential dy of the given function. (LUse "cx" for dx.) x +3 3x

A: We will solve the problem

Q: Evaluate the second derivative at the given point. dy If dx = 3 ey + x2, find at (4,0) dx2

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Q: The derivative of the function y = cos VI at z = is equal to 4

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Q: A particle moves along the x-axis with velocity given by v(t) = 3T sin (t) for time 10 at time t =…

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Q: 1. Given dx [arccot u] = find the first derivative with respect to x of arccot v2x + 2. 1+u?

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Q: Find the differential dy of the given function. y = x(1 − cos x)

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Q: 2. In each case, find the derivative d. (a) z = x³ – y² and x(t) = cos 2t and y(t) = e-3t, (b) z =…

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Q: Find the general solution of the equation dy + (tan t) y = cost dt

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Q: Find the length of the curve y = ln x from x = 1 to x = e.

A: Given:Find the length of the curve y = ln x from x = 1 to x = e.