Solve for dy/dx and d2y/dx2 of : y=(x^2e^-x)- 4e^x

Q: 2x2 dx 5 – x²

A: In the given question we have to find the integration by putting in the integral. So we will…

Q: Solve 2 sinh(x)– cosh(x)= 5 by using the definition of the hyperbolic functions.

A: We know thatsinhθ=eθ-e-θ2coshθ=eθ+e-θ2

Q: Integrate (sinx + cos^2x)^3 dx

A: To evaluate: ∫sinx + cos2x3dx Let I = ∫sinx + cos2x3dx ⇒I =…

Q: Integrate O sinh 2x dx

A:

Q: Integrate:  (5e^-3x - cos (6x))dx

A: Integrate

Q: et-x+l 2x –1 -dx by using substitution method. Integrate

A: First I have made a substitution and integral become easy and then solved . I have written all…

Q: ind dy/dx of y= tan^-1 (ln x^2

A:

Q: 1) [(sinh 2x + cosh2x)° dx

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Q: solve for dy/dx :  arcsin (x/y) + arccos(y/x) = 5

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Q: 2. COsh(4x)dx

A: We have to solve given integration

Q: ind dy/dx if y=8x-3/24x^5

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Q: Sinh) esechct) dy

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Q: Bind dy, 4. Ssinx.cosx sinx-coSX 1 +2.Ln X

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Q: sinh (:) dz dy dx

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Q: xe dx

A: In the given question we have to solve the integral s.t ∫xexdx. we will solve the indefinite…

Q: Find dy/dx by implicit differentiation 7ysin(x2)=9xsin(y2)

A: Find dy/dx for the implicit function

Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

A:

Q: solve for the intergral of (2sinx)/(1+cos^2x)dx

A: The integral to be evaluated is  ∫2 sinx1+cos2xdx. Here, we can use substitution method to evaluate…

Q: 3. x)dx sin(ln

A:

Q: Integrate sec√x dx ÷ √x

A: We have to Integrate : ∫secxxdx Let x=t⇒12xdx=dt⇒dx=2xdt=2t dt Now, ∫secxxdx=∫sec tt(2t dt)=∫2 sec t…

Q: Integrate  dy/dx sinx=1

A: We know, ddxcosec x = -cosec x·cot x ddxcot x=-cosec2x ddx(cosec x-cot x)=-cosec x·cot x + cosec2x…

Q: Find dy/dx by implicit differentiation. 3x2 - 3y2 = 16 %3D dy/dx =

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Q: Integrate: x² cos(2x) dx

A:

Q: Find ∫cosh 2x sinh2 2x dx.

A: To find the value of the integral∫cosh2xsinh22xdx

Q: find integral sec 3 x dx

A:

Q: Find dy ldx by Tmplicit differentiation. tanLx-y)=

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Q: Find the function that passes through the point (1,2) and whose derivative is dy/dx = (2/x^3) - 4

A: Topic:- application of integration

Q: Find dy/dx by implicit differentiation. 2x3 + 3y3 = 64

A: Given: 2x3+3y3=64 for finding dydx, we differentiate given expression

Q: dx Q2. Integrate

A: Given,I=∫1x2+15dx Consider x=tanu and u=arctan(x) then, dx=sec2udu…

Q: Use an appropriate substitution to integrate 12 x*(x++ 1)°dx

A: The given integral is 12x3(x4+1)9.

Q: sin“ (x)dx 4

A:

Q: Find:  ∫cosh^4 (x) sinh^5 (x) dx.

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Q: Find dy/dx by implicit differentiation. 4x° + 9y3 - 62 dy/dx =

A: We use Implicit differentiation

Q: Find dy/dx by implicit differentiation. x4/3 + yA/3 =12 %3D dy/dx = (Express your answer using…

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Q: aluc of 4 alue of dx. 1+(x – 2)? 1

A: See the details solution in below

Q: tanh 2x In (cosh 2x)dx

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Q: Integrate f sinh 2x dx

A: In this question we have to find Integration.

Q: 1+y* 3+ sec(y)

A:

Q: Integrate: cos Gx) – sinh(2x)]g

A: As per our guidelines only one question can be answered.Please repost the next part in next…

Q: 2 S Sec'x In cotx) dx (

A: We will solve the problem.

Q: Find dx if 2 siny dy 3 Log (y1)

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Q: Integrate: xー1 dx 2.

A:

Q: how do i implicitly differentiate (solve for dy/dx) where: xy = tan(xy)?

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Q: - S sech-x tanh x dx 1 2 2

A: From the given problem: I=∫sech12x tanh12x dx=∫sechx2 tanhx2 dx....1 As we know that:…

Q: Integrate completely

A: Given,             ∫2x+12x-53dx

Q: Find dy/dx by implicit differentiation. 2x2 - 2y? = dy/dx =

A: We can get dy/dx by differentiating both sides w.r.t x. The solution is explained in step 2.

Q: Se Sin (3x) dx by Improper htegrations.

A: use improper integral

Q: 8. Scoth 2x In (sinh 2x) dx

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: