(17) = ² × ( ¹²7 ) = ² × x=(²7)e²+(²1) ²² = ₁₁ (²₁) e² + c₂l(¹) te² + (1) e¹ dx dt dy dt O 2x + y -X X = a₁(²¹₁) e² + c₂l(¹₁) e² + (9) e'] X = ₁₁ ( ₁¹₁ ) e ² + ₁₂ ( ¹₁ ) e²

Q: Find g'(x) if g(x) = t² cos 6t dt %3D 2

A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: 1 23 515.2 1 Calculate AT A and AT b, given A = 1 11 and b = 13 293.8 329.8 1 4 178.6 AT A = Ex: 1 :…

A:

Q: If x = tan - log y a d'y dy Show that (1+x²)- +(2x- a)-0 dx dx?

A:

Q: Let v = (5 — 2xyz — xe² cos y, y²z, e² cos y) be the velocity field of a fluid. Compute the flux of…

A:

Q: JO (5) Find the derivatives (a) d # t ( * cos(2³) dz + 35e) 4

A: Since you have posted multiple questions i can do first question as per our company guidelines.…

Q: / 11 (2xy- 1) dx + x² dy = 0; (1) = 2

A:

Q: • A) Ln(y²+1)dx+ 2y (х-1) y²+1 dy = 0 B)Y = x/1-y2 dx C) xdy-ydx-x²y'dy=0 %3D 1+x2

A:

Q: (B)(10M) Evaluate (y(x)) dx y(x) = cot (csc(sec(In x))) %3D

A: derivative

Q: A curve y = f(x) have length of the curve from x = 0 to x = 1/2. dy Vcos(2x – 2) as its first…

A: We have to find

Q: 2. Solve 3 y'(z) + y(x) = y²(z) (cosz - sinx)

A:

Q: Find the derivative of (a) (교2 + 1)" (6) In(cos²(e2")) 2x (c) sin-1 e-1 dt x +1 In a

A:

Q: (A) Evaluate / (4x – 5) (4/x + 4x) dx. x² + 3x - 6 (B) Find dy -, if y = 3 -)4 when x = 1 %3D dx

A: *we have to perform integration operation in A & differentiation operation in B.

Q: 4) Solve (xe + ye" )dx+(xe" +e' )dy = 0

A: The differential equation is xe-y+ye-ydx+xe-y+eydy=0 Write it as: e-yx+ydx+x+e2ydy=0x+ydx+x+e2ydy=0…

Q: Suppose f(2) = 4, f' (2) = 5, f(8) = 8, f' (8) = 2, g(2) = 4, g' (2) = -6, | dH and H(x) = f(x² +…

A: Topic :- Derivative

Q: Suppose f(2) = 1, f'(2) = –6, and | dH H(x) = (1 + f(x))³. Find dx Н (2) %3

A:

Q: Find dy/dx ln(x+y)-cos2y-x^2=0

A: Revise this before doing the question:

Q: 1 dx (b)

A: Given interval :

Q: 35. A particle travels along a curve y = f(x) as in Figure 15. Let L(t) be the particle's distance…

A:

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: (ii) y = e2x cos(1+2x²) (1+2x²)

A: y=e2xcos1+2x21+2x2

Q: F(x) = J e2f sin² (3t)dt. Then F'(x) =

A:

Q: Find dy/dx for y = 3l(sin-(e-3**)12 dy 3(sin"(e-*)* In3 2(sin-"(e-3x*)- dx 1(-6х) V1-e-6x2

A:

Q: y'' - 15y' + 60y = e^x cos(16x

A:

Q: f(x)=cos(x) Glx)こxや+1 d f(9(x) = t3 clx

A: We have to find derivative

Q: (1+x)y' + y = cosx; y(0) = 1

A:

Q: rez If F(x) = -7 sin t dt, then F'(x) =| %3D In x

A:

Q: (g) sin vt dt.

A: Intigrating the given equation.

Q: Solve y" + 2y + 2y = e cos(x) with y(0) = y'(0) = 1.

A:

Q: (e) (x² +x)dy = (x' +3xy+3y)dx %3D (f) y" +2y' = 4x %3D

A: For first problem i have solved using integrating factor.  For second problem i have find cf and pi

Q: (2xe" + e*)dx + (x² + 1)e'dy = 0

A:

Q: Ex (1): Solve (D'+4)y = e cos 3%

A: Solve the following

Q: Y ay dx log3 (x² +1+2 cos x) Compute for

A: according to bartleby guide line we do only first part of multiple questions  given y=log3x2+1+2cosx

Q: In (2x) ty= S sin (3e') dt. fy D

A: Given fy=∫0ln2xsin3etdt