find 45. dx x3/2 – Vx 46. dx 1) Vx (Hint: Let x = uº.) (r'/3 - Vx + 1 47. - dx = dx 48. JxVx + 9 (Hint: Let x + 1 = u².) dx 49. J x(x+ + 1) dx x°(x° + 4) 50. Hint: Multiply by 51. dθ 52. de cos 20 sin 0 cos 0 + sin 20 Vx V1 + Vx dx 53. 54. dx V2 – Vx + Vĩ х

Q: Let y = tan(2x + 2). Find the differential dy when z = 5 and dr = 0.2 Find the differential dy when…

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Q: Let y = tan(4x + 6). Find the differential dy when x = 3 and dx 0.1 %3D Find the differential dy…

A: Explanation is given below...

Q: Evaluate the line integral / (9x + 10y)dx + (5x – 6y)dy along the curve C : a = 6 cos t, y = 12 sint…

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Q: dt 34. tan t/4 – sin² t dy - Vy dy 35. 36. yV3 + (In y)? x² 1 38. dx 4х + 5 37. :dx /x² + 2x + 5…

A: 34) Solve the integration:

Q: dx dy Find at x = 1 if y = – 5x´ – 3 and 5. - dt dt dx dt

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Q: Q1/ Evaluate So (x² + 3y²) dy dx using Simpson's 1/3 rule in x-axis and Simpson's 3/8 rule in y axis

A: 1 Given integral is ∫03∫01x2+3y2dydx. We have to evaluate the given integral  by using Simpson's 13…

Q: Q3) Find dy/dx if 1- y= In x 2- y=x sinx+1-x

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Q: 2(y+1) dy t 2) 2(у + 1)4 dx x+1

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Q: Find dx/dt given that 4x^2+9y^2=13x  x=1,  y=-1 and dy/dt = 10

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Q: Let y = tan(2z + 3). Find the differential dy when z = 2 and dæ = 0.4 Find the differential dy when…

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Q: dy/dx if y = cosh 2 Jx +1 2 JX +1

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Q: dy Find at x = dt dy dt || 4 if y = 3x² + 5 and dx dt = 1.

A: Let's find dy/dt value at x=4.

Q: dy Determine the general solution of = 1+ 3y tanx. dx

A:

Q: Let y = tan(5z + 6). Find the differential dy when a = 4 and dæ 0.1 %3D Find the differential dy…

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Q: dy Find for three only: dx 1) y = In(cos x . Inx²)

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Q: dy dt when x = 2. Let xy = 3 and Find dx dt 5.

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Q: 1- Evaluate: 2y sinx dy dx อน 2- If u = x² + ey², x = sin 2t , y = cost² find Ət

A: Above question is solved.

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

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

Q: Find dy/dx, where xsiny +ysinx=1.

A: Given - xsiny+ysinx=1 To find dydx Here we will use the following formulas- ddx(uv)=udvdx+vdudx…

Q: Find dy dx 21) tan y = eX + In 4x eX + 4 A) - sin² y хeх + 4 B) - xcot y

A: Given;  tany=ex+ln(4x).

Q: In(5x +3) dy at x = 0. dx (a) If y = then find et

A: Given; y = ln(5x+3)/e5x

Q: Let y = tan(4x + 6). %3D Find the differential dy when x = 5 and dx: 0.4 %3D Find the differential…

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Q: dy dt 1 if 2y°t + t°y = 3 and dx Find dx cos t dy dx

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Q: Suppose y = square root 2x + 1 where x and y function of t . A) if dx/dt =12 , find dy/dt. When x= 4…

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Q: Find the particular solution for the given separable equation when y(0) = 3. 1 dy = ysin(2x) 1? dx

A: To find the particular solution for the given separable equation when y(0)=3

Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x day 6. dx if y = 1-cos4x 1+cos4x dx² dy 7. a if y = In…

A: (7) Let y=lnsinh 5θ and x=cosh(4θ)

Q: Use the Euler method with dx = 0.2 to estimate y(1) if y' = y and y(0) = 1. What is the exact value…

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Q: Use Leibniz's rule to find dy dx dy dx for y= 8x-1 √ (t4-5) dt.

A: Concept: Newton Leibniz Theorem : Newton Leibniz A formula for differentiating a definite integral…

Q: dz Find dy x sin(2y – 5z) =1+y cos(6zx)

A: Given x2sin2y-5z=1+ycos6zx. To find ∂z∂y.

Q: Evaluate the line integral (5x + 8y)dx + (3x – 5y)dy along the - curve C : x = 10 cos t, y = 20 sin…

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Q: Let y tan(4x + 3). Find the differential dy when z = 3 and dx = 0.1 Find the differential dy when r…

A: y=tan4x+3

Q: Find dy dx if x=- and y and %3D dx 1+t 1+t

A: Given: x=t1+t and y=t21+t.

Q: For y= sintx/2 obtain dy/dx at x= 0.5 with Ax= 0.1 using: dy。+1-リ-1 (a) dx 24x dy Yj+1-Y;. (b) dx 4x…

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Q: Find dy/dx implicitly exy+x2−y2=19

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Q: Let y = tan(4x + 4). Find the differential dy when x = 5 and dx 0.4 %3D Find the differential dy…

A: Given : The function y = tan(4x + 4)   To find : Differential dy when, 1. x = 5, dx = 0.4 2. x =…

Q: Find the general and particular soulution of dy/dx=3y, where y=6 and x=0

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Q: 5 dy of: y = |x sin 2 + tan (x") dx 4

A: Given function is y=xsin2x+tan4x75 We have to find dydx. Here, we have to use some rule of…

Q: B. Verify that dz/dy dz/dx 1 =. If xy + z = sinz.

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Q: dy 2) Find implicitly: dx (a) xy+3x2 =y? (b) exy – Iny =x? %3D

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Q: 2X Qul If y = Fird dy e %3D (x? +1) (I+ sinx)

A: We use logarithmic differentiation

Q: Find dy/dx of x siny + y = 4x + 3

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Q: Let y = tan(3x + 8). Find the differential dy when x 5 and dx = 0.4 %3D Find the differential dy…

A: First differentiate then put the values

Q: If x ^2+ y^2=100 and dy/dt= 4 , find dx/dt when y =6

A: Solving the problem by method of differentiation.

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: Find the differential dy when x = 3 and dx = 0.2 %3D

A: When you get function of function form to differentiate, we use the chain rule. y = f(g(x)) dy/dx =…

Q: Evaluate the line integral (6x + 8y)dx + (3x – 3y)dy along the curve C: x = 4 cos t, y = 8 sint…

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Q: Find dy/dx implicitly. exy + x2 - y2 = 10 dy dx

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Q: Find dy/dx implicitly. exy + x2 - y? = 11 |

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Q: dy for y = dx 9t -dt. 9t + 1 iz's rule to find

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Q: y = In(x +1)

A: Given that : y = ln(x2 + 1). Find dy/dx  We know that derivative of - d(lnx)/dx = 1/x. And d(xn)/dx=…