Prove that Ho Ge) =(-1) e" ď e dx 2. 2.

Q: Find the exact value. In 3 0 ³ sech 4 x tanh x dx

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Q: find dy / dx by implicit differentiation.

A: In implicit differentiation, on differentiating y, we use dy/dx.

Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: > Evaluate the Antegral dx ax45x +2

A: Rewrite the given integrand as follows. 32x2+5x+2=32x+1x+2=22x+1-1x+2

Q: 70ot(*) e*dx e2x +1

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Q: What is dy/dx of 1/2e^2x

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Q: Find

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Q: I = | In(ax + 1) dx, for a > 0

A: Find the integration of I

Q: Prove that  d/dx[cosx]=-sinx

A: We will use the definition of the derivative  Here f(x)=cos(x) So,

Q: nasin(hx) cos(bx)dx

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Q: Obtain a-(In x)? dx.

A: Given,  ∫x-5(lnx)2dx

Q: sinh In(2+2x) dx? x+1

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Q: If y- sinhx then prove that = dx

A: Fundamental inverse Trigonometric Identities: →cosh2y - sinh2y = 1 Basic derivative:…

Q: 2 dx =

A:

Q: In Exercises 1–12, find dy/dx.

A: Question 7,Given,          y=cotx1+cotx

Q: dy log x If xY = ex-Y, prove that %3D dx (1+ logx)?

A: Introduction :

Q: Find e-ax dx } first integrating and then transforming result.

A: Here we find Laplace transform

Q: The integ ral csc(0.5) dx is equal to

A: Follow the procedure given below.

Q: Without integrating, explain why: S, ?)°dx = o x(1+ x* -2

A: To show:     ∫-22x1+x22dx = 0 (without integrating)

Q: find dy / dx by implicit differentiation.

A: Given equation is x4y-8xy+3xy2=9. To find dydx. Solution: Power rule of differentiation states that:…

Q: in integrating the function fx cos() dx using intogration by parts, whut would you choose for your…

A: Solution

Q: (b) Show that 2t cos x and sin x = 1 + ? (c) Show that dt dx 1 +

A:

Q: arctanx e dx (1+x²,"

A: The given problem is to evaluate the given integral. We have to evaluate by using substitution…

Q: dy Find by implicit differentiation. 20x = 20 - ey ... dx (Type an exact answer.)

A:

Q: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

Q: d - In(u²) dt dx et

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Q: please solve determine dy/dx if xy = ecsch(xy)+πcos(0)

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Q: d tanh (u) du Sech (u) dx dx

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Q: Use x = e to explain why dx (In x) = = -, for x> 0.

A: To differentiate x=ey, with respect to x, use the exponential function rule, ddxef(x)=ef(x)ddxf(x).…

Q: What is the derivative of y = e3 In(5 + e3)? %3D

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Q: If y- sinhx then prove that dy dx

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Q: tan '(z) Find for y = In( - dy dz You do not have to completely simplify!

A: topic - derivatives

Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

Q: Integral of e^(4x)sin(4x) dx

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Q: Use an appropriate substitution to integrate 24xcos(x2-2)dx

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Q: Jrin m In(cos m) dm

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Q: tan st e dt 2

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: dy Find by implicit differentiation. dx 6xe + ye = 7 dy dx

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Q: Find at the point (1,0) for cos xy + ye* = 0. dx

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Q: dx Evaluate

A: ∫0919+x2dx

Q: Show that ∫∞−∞ sin x dx diverges.

A: To Show: ∫-∞∞sinxdx diverges.

Q: cosh(In x) dx

A:

Q: Compute dx in two ways and verify that the answers agree.

A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

Q: In (sinh x ), + tanh x j + 1-x k )dx 1- sinx

A:

Q: x sin 2x sin cos x 2 X. Prove that 8 dx 2х - л

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Q: In(3) In(3) dx dy y/2

A: on solving this we get

Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

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Q: What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.