What is the A B (C) D af - of f (x, y) = tan (x²y³ + 2xy)? dy [ sec 2 (x2y3 + 2xy (2 xy + 2y) 2 [sec ² (x²y³ + 2xy] (3x²y² + 2x) [ sec 2 (x²y³ + 2xy] (6xy2 + 2x) (²7¹) + xy 4 [sec ² (x²y³ + 2x y ] 2 4

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A: We have to prove the given differential equation to be true.

Q: y = tan(x sin x) O (x + sin x) sec² (x sin x) O (x cos x + sin x) sec² (x sin x) O (x + sin x) sec(x…

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Q: Q6:-Prove that: y" =1 y =csc(tan"") if

A: Given y=x4·csctan-114x2-1 Let tan-114x2-1=α ⇒tan(α)=14x2-1 ⇒cscα=2x ⇒y=x4cscα⇒y=x4(2x)⇒y=x22

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Q: Q3 Find and show the work for (x+3)(3x+2) dx. (a) х (b) F (sin(2x) – cos x) dx. (c) S(3x² + 2x +…

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Q: The integraing factor of (4xy+3y² – x)dx + x(x+2y)dy3D0 is (A x-2 B 2x-2 2x-1 D D x2

A: Since, the given differential equation is not exact . To make it exact we find integrating factor ,…

Q: Q.2 Differentiate the function y = 2x - 3x + 4 2) y = xcosx 3) y (1 + x2)3 sinx 4) y = 5) y = tan x…

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Q: Function dy du dy du dx dx = (5x³ – 7x² + 2x – 3)*) _y = csc(x² – 3) y = 5x² – . y = V5x2 – 4 _y =…

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Q: (D³ - 3D2 + 9D + 13)y = 0

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Q: Q# (13 Rewrite: cos (x)sin(x)dx A) ſ u'du 1/2 B) Tu°du V312 C) [ -u°du 1 V3/2 D) [ u°du 1 V3/2 E)…

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Q: Question 2 * SE sec2 (0) d0 = dx a) sec² (x³) - 3x² b) – sec² (x³) · 3x? | O ) sec² (x³ ) d) – sec²…

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Q: -1 Let f(x) = (3 sin z + 4 cos z)tan f'(x) = %3D

A: Given  f(x)=(3sinx+4cosx)tan-1xTo find f'(x):

Q: Vỹ - 2 dy (b). / ž r64 7. Evaluate (a). tan(4x + 9) dx

A: Given: To evaluate a) ∫164y-2y3dy                     b) ∫13tan(4x+9) dx

Q: Q1) Evaluate: (a) fe²_1_dx Inx sin ¹x 1-x² dx (b) f 1- cos dx (e) Jỗ 2sinx cosx dx (c) | Inx dx

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Q: dy 1- Which one is correct ? The Y of ex?tanx a) (x2 sec?x tanx + 2x tanx) b) (x² sec?x + 2x…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: ¡ sin √x √x dx 18 tan² xsec² (2+tan³ x)² dx

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Q: (D2 -4D +7)y = 0 A y = e²"(c,cos/2x+c,sin/2x) COS y = e2"(c,cos/3x+c,sin/3x) В © y = e (c…

A: 1. Given differential equation is (D2-4D+7)y = 0 Here Auxiliary equation is D2-4D+7 = 0⇒ D = 4 ± 16…

Q: Evaluate tan" (x) sec4x dx. 1 1 (A) =tan(+3)(x) + _____tan ( + 1)(x) + C m+3 m+1 1 B) (m+3 -tan…

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Q: Find the analystic function f(z)u+iv if u=a(1+cos0)

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Q: 故(x3+5) ex A al d Iny d in5x

A: According to our guidelines we can answer only three subparts, or first question and rest can be…

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A: Using tan(A+B) =( tan(A) + tan(B) )/(1- tan(A) tan(B) ).

Q: Let Then dy dx = y = tan-1 √4x² - 1)

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Q: 6. Find : (a) y = (x³ +5) tan 7x, %3D

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