2x [In sin to where in #2, V=In sing y-x (1-x²)]|dx + (1-x²) cot y dy dv=; du shy cosy dy = coty dy sin

Q: Find the GS of y" + y = cos x + sinx

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Q: Q Find dY 2. カー×* * (sinx Cosx) Q@ sinx cosX ® (sinx) Ofan Ctanx)

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Q: y" + y = cott

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Q: Activity 3: 1. ſx²dx 2. SVx?dx 3. S(x³+x²)dx 4. SVx*dx 5. fx-2dx 6. S tan?x dx 7. S(1 – cos u)du 8.…

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Q: Find y'. cot (1) y = 4 cot O A. O B. -8 csc (*) 4 9 CSC 9

A: Given:; Now,           y'=4cotx9'     =4cotx9'     =-csc2x9x9'      =4-csc2x919     =-49csc2x9

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

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Q: tan 0 d 30. dO sec² y dy

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Q: e-i.dt = lim X+ 00 V TE 0, Select one: a. b. NOT C. 8, O d. 1 O e. 0

A: According to our guidelines we can answer only first question. In first question we use the concept…

Q: Find y". y = edx sin Bx y" =

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Q: cos 2y + 2x3 = 5 − 4y2ex

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Q: y*dxdy V2 y у?)2 2 3/2 (x² +

A: Here we have to evaluate I=∫01∫0yy2dxdyx2+y232=22

Q: Differentiate the function y= 1-ex #48 y= e + Sincee) Cin2x

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Q: INIL Find in sin (1 + 2x) + xy = ecosy dy dx

A: We need to find derivative.

Q: find ody dx 4= Sin 3X

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Q: dy (2x sin h -+3y cos h -) dx Зх cos h - 2 tan h 3 + ||

A: According to the trigonometric hyperbolic formula: tanh(x)=sinh(x)cosh(x)        ...(i) Distributive…

Q: 6) By implicit differentiation find a) xy + y² = 2 find d²y/ dx² %3D b) sin(x²y²)= x find dy/dx

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Q: Find when y = cos(sin 2x). ay dx dy dx

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Q: iii) a) Prove that Pa(-x) (-1)".Pn(x) u (2n)! 22 (n!) b) Prove that P2n(0) = (-1)".- %3D

A: To prove- Pn(-x)=(-1)n.Pn(x)P2n(o)=(-1)n.(2n)!22n(n!)2

Q: Use Trigonometric Substitutions dx 1. xVx +16 x*dx (x² – 1)"2 2. 3/2

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Q: 1. Find dx dy for the following functions: 1) y = (x- 3)(1- x) (ans.:4 - 2x) b (ans. :-,) x* 2) y=…

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Q: ) dx dy is

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Q: dy Find by implicit differentiation, where 2x7 + 7x³y – 6xy" = 4. dx dy dx

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Q: Let 7 sin x + 3 cos y = 6. dy dx 0 -0 ď²y dx²

A: The details solution of the given question is given below in step 2.

Q: find af/ax and ðf/əy +4- 17. f(x, y) = sin² (x – 3y) %3D

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Q: Evaluate:

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

Q: sin x cos x dx 4

A: We have to evaluate the given integral.

Q: y = sinx, x = 0, y = 1; about y = 1.

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