3. X-メ Find d x at x=\

Q: | (In x)" dx = x(In x)" – n[ (In x)"' dx n-1

A: Use integration by parts

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Q: Find d if z = log2 y - 6 logs y. In In 64 dz dz dy y In 2 In 5 dy y In 2 In 5 O Option 3 O Option 2…

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Q: Differentiate. y= In [(x + 4)(5x– 6)(3 – x)] d dy In ((x+ 4)(5x – 6)(3–x))) = |

A: Given: To find: The derivative of the given function.

Q: Find G'(x) In(8) (4e 6t 1) dt G(x) х G'(x)

A: Given:

Q: Compute (d/dx)(∫_-x^x(e^s2ds).   Compute (d/dx)(∫_0^x2sin(s2)ds).

A: In this question, we find the derivative of the given integrals. In these questions, we have used…

Q: 1. Evaluate L²S³ (2y³ + x²y) dx dy

A:

Q: 19) * (xy)* = e ; f ind y' y' = [1+ In(xy)I y' = -y [1+ In Option 2 O Option 4 y' = [1- In(x None of…

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Q: 뿐 for the following: y = ln(e2z) 0 읊 ○ 2 Oezz ○ ez (In 2)

A:

Q: S S" x²cos(xy)dxdy

A: To calculate the integral: ∫01∫0πx2cosxydxdy

Q: 1 2 S S xe dx dy ху хе 0 -1

A:

Q: 1 11z Evaluate ſ dz [ dx

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Q: 4 2 S[(x) dy dz 0 0

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Q: If y = e Oe3 Oe 3x X² O 2e3 O 3e³ then dy dx at x = 1 is

A: To find derivative of given function at x=1

Q: dey こてxニコッン alx

A: We have to find :- d2y/d2x= ?

Q: Compute ∆y and dy for y = x^2 − 4x when changes from x = 3 to x = 3.5.

A: Topic:- application of derivatives

Q: 2. Find (x) which satisfies (4e y − 1)dx + e dy = 0. O p(x) = e¯² + 5e-4x O p(x) = 3e e-4x O p(x)…

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Q: 1. Evaluate S xe0.1% dx In x 2. Evaluate Sdx x3 3. Evaluate S x³(x² – 1)1°dx | 4. Evaluate (2 +…

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Q: Question 9 Evaluate: 3x* In(x) dx x + -x In x) + c

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Q: 1. Find x'e *dx if it exists.

A:

Q: 2. Suppose f(x) dæ -5 and f(x) dx = 6. Compute 2f(x)+ (3x – 4)² dx.

A: Answer is 41 Explanation is given below

Q: Use geometry to evaluate the following integrals.

A: Given: fx=2,0≤x≤53,5<x≤10 we know that ∫010fxdx=∫052dx+∫5103dx…

Q: In x /1+ (In x)² 6 S -dx

A: Given query is to eveluate the integral.

Q: 3 Evaluate: ₁ S 1²,₁ S² [(x²-x²)²] dx dy x+y

A: To evaluate the given double integral.∫-14∫03x2-y22x+y dx dy

Q: 1. Find dy dx S(x)= e**/2x-5 (6-5x)* (iii) f(x) =

A:

Q: 4. If ( Inx dx = f(x)[In(x) + 1] + C, then f(1) = A 1 B D -1

A: Solution

Q: 5. LL dx x In x A. Iln x| +C B. In/x|+C C. In|Inx|+C OPY D. +C In x

A:

Q: 4х Compute dx Vx2+1

A: Given,           ∫354xx2+1dx

Q: 17. If y = x, then dy/dx (a) x²-² (b) x²-1 lnx (c) x²²(1-In² x) (d) x²-²(1–In x) (e) None of these

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Q: .2 Evaluate: xye dy dx 0 J1

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Q: 1. f o¬* xy dy dx О а. 32/3 O Б. 16/2 Ос. 32/4 O d. 18/4

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Q: if : 1 1 + + 1+x² ' 1+x° 1 t...+Tx" 1 f(x)=1 1+x a+1 a+1 and / f(x)dx=2 then find : / f()dx = ?

A: using the given value of the function and definite integral we need to evaluate the unknown value of…

Q: d (e¬× In x) dx e-x e-x ln x – e-x e-× In x + O Option 1 Option 2 e-x e-* + X In x e-x +

A:

Q: find dy/dx of the following:

A: Please refer to the image below

Q: If y = (1 + x)(1 + x²)(1+x*)....(1 + x* ) then at x = 0 is - dx

A: Introduction :

Q: 4. (a) Find (b) Hence evaluate d dx √1+x² X S (1+x²)³/2 dx.

A:

Q: 4-compos dx dy 5-find dry if f(x, y) = xe xe 6- find (x²³/2)

A:

Q: 5. fx² In x dx

A: See the details solution in below

Q: 1. Solve (6re",x0 b. [3cos 2xsin 7.xdx

A: here we have to evaluate  a) ∫-11w(x)dx if w(x)=6x2ex3,x≤035x-3 , x>0b) ∫3cos2x sin7x dx

Q: 1. Evaluate the integral: x/x – 1 dx.

A: answer = 1.0667   explanation is given in below step

Q: 1 1 Evaluate f dz[ dx [ e dy. бе/3 (бе-б)/3 О бе-6 6/3

A:

Q: Show that (In x)² dx = e – 2 Find ſ dx x2+ 5x+6 4х Find f dx (x2 – 4)(x-3)

A: Given that  The following integrals

Q: (2) Compute dy dx if mxy=55

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Q: (1 + 1 1 + In(x) + - X (x+y)ln(x) - 5y = c dx = (5-In(x)) dy

A:

Q: 5) [2x + ycos(xy)]dx + xcos(xy)dy = 0

A: Given: 2x+y cosxydx+x cosxydy=0 To Find: To solve the given differential equation.

Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

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Q: 8). S coth 2x csch 2x dx (Apply u-substitution method)

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Q: 1-x2 So Si S dz dy dx 0. 0.

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Q: -1 x-x2 dx -8 2도 1423 1521 22 20 Option 1 Option 2 1425 1523 22 20 OOption 3 Option 4 None of the…

A: Given problem:-

Q: 1. Evaluate xy Vx² + y² dy dx 00

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