Find dy each of the following questions. dx In(1-e*) а) у 3D x2 b) x2у — у2 %3D 3х3 + еx

Q: 7. Find dy dx (a) y = (x* + 5x) cos 5x, %3D

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Q: dT 4 dp = 0; Pdp pdT T = To when p = Po

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Q: The dv of sin-lx dx is dx. A) True B) False

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Q: dy If dx = COS s 2x, then what is y?

A: The derivative is given by dydx = cos2x                         ........(1)

Q: F ind So S. eu dy dx.

A: Use the concept of reversing the order of integration. While integrating with respect to one…

Q: solve D.E. by using homo. xsin-- ycos-) dx + xcos-dy = o

A: put y=vx dydx=v+xdvdx differential form  v+xdvdx=vxcosv-xsinvxcosv take x common and split the…

Q: 4. Find d?y/dx² for the following functions: b) y = cos*(sec² 3x)

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Q: (2х — 3)* y = - х +1 .2 х*у + 3ху3 — х %3D 3 X =

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Q: dy If x = sin? (u) and y = cos2(u), then %3D dx

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Q: d (b) [arctan u] - %3D dx 1 + u?

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Q: Given z 10 In(t) and y- 100 t then find dy da d'y da?

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Q: dx Given that the substitution. u=lnx xlnx True False

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Q: Simplify the expression shown.

A: Given:

Q: and du' dx Find xp (a) y = u5 and u = x² + 2 Ap du du dx dy xp II

A: Part a,Given,          y=u5 and u=x2+2.

Q: Specify the order and degree of the following ODE /2 d'y dy 1+ dx = y- dx2

A: Equation that gives the relation between variables and there derivatives is called differential…

Q: dy Find for y = sin (2x +3) da %3D Ans=

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Q: Evaluate the following and post your answers in (Activity 2.1) 1.dz 2. Sa dx 3. S(7y6 + 8y – 1)dy

A: 1. ∫13dz=13z+C2. ∫a3dx=a3x+C

Q: In Jx2/25+ x² dx , we let x= 5sine. A True B False

A: Note Since you have asked multiple question As per our policy, we will solve the first question for…

Q: Suppose d a e R, where a > 0, a ± 1, what is (a*]? dx

A: Given,            Supose a ∈ R, where a>0, a≠1.To find : ddxax

Q: (In x)² dx, .3 te ato u a ? and dy

A: Integratipn by parts problem

Q: Given y - xy? – x²y=2. Then, at the point (1,2), -is dx Blank 1

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Q: Show | S a² sin®(e*) dæ| < 16n*. 8 Show | S, x2 sin°(eª) dx| < 3

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Q: S = ÷ S gle) de, then 9 x /1 - xª dx 4

A: The question is taken from the calculus in which we have to solve the integral of given question We…

Q: Q4) A) Determine the following 1)√√²/1dx 1)ƒ cosxdx 2) S dx 2+3sinx

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Q: Find dy/dx for the following : (Invx) (4secx) (tan-le3*) (6cot5x) e(2 In 9x) 13) у %3D

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Q: the solu dy + 4: dx

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Q: dy IN QUESTIONS 1-13, FIND dx' 3. у %3DV11 — бх

A: Given that       y = √(11-6x) We have to find dy/dx .

Q: Find dy dx? A) y = 3sin u - sin'u and x 3 cos u- cos'u

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

Q: Suppose a E R, where a>0, a + 1. What is dx A a* B xa*-1. In(a) ха xa*- a*. In(a)

A: The objective of the question is derivative of given function.

Q: Suppose a E R, where a > 0, a # 1, what is[a"]? dx a" In(a) © xa²-1

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Q: dy 5. If y = e3+1 sin(1 – a²), then Find da

A: We have given y=e3x+1sin1-x2 We have to find dydx.

Q: Find the number m, such that the function y = ema is one solution of the ODE dy &y dy + 5- dx? = 0…

A: We will satisfy the solution with given ODE to get value of m.

Q: 7 Let y Find values for A and B so that dy dx A where A B = || ||

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Q: ,2 4 +(dx dt 2 dt ....

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Q: Exercises: A. Find for the following: dx 1.y = (5x+3)6 2. y = sec(2x) + tan(2x) 3. y = In(x²-3x - 1)

A: To find the derivative of given functions.

Q: у?dx + (ху — 1)dy %3D 0

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Q: Evaluate J2 e* cosx dx 0.

A: To evaluate: The definite integral ∫0π2ex·cos x·dx. Concept used: Integration by parts:…

Q: Determine if the equation 2xy dx + xy dy = 0 is exact. Identify M =O and N=O

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Q: dy If y = e", then = nen-1 dx A) True B) False

A: Let's find.

Q: 3. Find dy of the following equations: dx a. y = |(e-3x² + 7x² + In 8x

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Q: -dnd auf for the feaoy) =tan Cx+y). 3xし y

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Q: Which of the following is correct? dx dx 2 + C 3x 1 Arcsin* + C 2x { A} S = Arcsin: {C} f V4-9x2…

A: Option C is   correct Answer

Q: 3 T - 2 Evaluate: J. Soves y cosx³dy dx

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Q: integrate the following:  Ue the U-substitution. ∫3/(√4x2-12x+9) dx

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Q: Evaluate: . dz dy dx x4+4 O T/24 O T148 O tan-(2)/24 O T/96

A: To evaluate ∫02∫0x3∫0y zx4 + 4 dz dy dx

Q: If the substitution U = Jx is used, then S dx is equi valent to ?

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Q: a) I= [In(l+x)dx

A: We have to find out the integral

Q: Evaluate 8xyz dz dx dy

A: In this question, we have to solve the triple integral in order.

Q: Solve the following IVP: dy sin(z*)e %3D dx y(2) = V5 %3D

A: Use separation of variables method on dydx=sinx2ex3 dy=sinx2ex3dx Now integrate both sides without…