Find the solution of the equation y^' = (1+y) sec ⁡x + tan⁡ x. and, Solve the equation x dy - y dx = 2x^3 dx.

Q: Differentiate y = /sin(x² + 3)cosx

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Q: Can we solve following differential equation by separable variable method dy y = eV+sinx secx %3D dx

A: Given differential equation is as follows : secxdydx=ey+sinx……1 Let Fx,y=dydx If Fx,y can be express…

Q: ५ = (+गुंग्ट

A: Given- dydx=1+y2ex To Find- The solution of the above differential equation.

Q: y = 2 ||

A: We have to find the derivative of the function y = 1-x2ex2

Q: Find  dy dx by implicit differentiation. tan−1(4x2y) = x + 5xy2

A: tan−1(4x2y) = x + 5xy2 We differentiate both sides with respect to x using the product rule and…

Q: Date: an ordinary By using suitable method differential equation by eliminating from the equation…

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Q: Arcsin(x/y) = 4x + 3y

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Q: Find  y ″  by implicit differentiation. 2x3 − 5y3 = 5

A: We will differentiate w.r.t x twice using the product rule and the chain rule

Q: Find the derivative of y=cos4 x sin4 x Ans: 1/2 sin3 (2x) cos cos (2x) solution?

A: We simplify the given expression using the double angle property

Q: 2sin x -1 2. y = cosx+ 2

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

Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: #11, find dy/dx by implicit differentiation

A: Differentiate question 11

Q: 4. If y = x cos x determine the 5th derivative. [y(5) = (60x – x³) sin x+ (15x² – 60) cos .x]

A: To find out the fifth derivative.

Q: 13. Find the second derivative y “ of y = 5z2 +sinrcosz

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Q: 6. y%= arcsin a Va2-x2

A: Given: 6. y=xa2-x2-arcsinxa

Q: 을 [ ] d dx tan-1(x)| 1+x?

A: To find derivative of arc(tanx) , we have to use some trigonometric identities and basic inverse…

Q: 40 60 100 What is the derivative of y(t)?

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Q: y = sec (2 – 3x)

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Q: Find y''' (3rd derivative) of y = sin^2 (tan(6e^x))

A: Here,              We have given a function and we have to find its 3rd derivative.         So , the…

Q: Find dy/dx by implicit differentiation. 5 5 y3 dy/dx = (Express your answer using positive exponents…

A: We have given 5/x^3 + 5/y^3 = 1

Q: Find the first derivative of y = Arc tan √x² −1+ Arc csc x 2 O 2 O 0 2 Ox√²+1

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

Q: Find dy/dx by implicit differentiation. x4 + yA 5

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Q: what is the derivative of this question with solution y= csc (4x² ) Arccsc (4x² )

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Q: The integrating factor of the linear differential equation – (tanx)y = x is_ - O sinx O log(cosa)…

A: Given dydx-tanxy=x

Q: Solve the problem and give a detailed solution. Find the 3rd derivative of y = sin(ex)

A: y = sin(ex) Differentiate w.r.t.xy'=ddx( sin(ex) )y'=cos(x)ddx(ex )y'=cosexexDifferentiate again…

Q: Solve ∫xn ln x dx in tegration by Parts?

A: Given:               ∫xn ln x dx Apply integration By Parts:              ∫xn ln x dx=ln x∫xn…

Q: y = csch /sec(x³ + 2)

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Q: Find the function that passes through the point (1,2) and whose derivative is dy/dx = (2/x^3) - 4

A: Topic:- application of integration

Q: find the second derivative and simplify the final result. 3. 4ln(Arctan x) = 1-y

A: The given function is 4lntan-1x=1-y It can be written as  y=1-4lntan-1x Differentiating with respect…

Q: Find the differential equation of family of lines whose angle of inclination is 60 degrees.

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Q: FIND THE FIRST DERIVATIVE OF THE FUNCTION cos r. y = cosx О а. SIN3X O b. - COS3X О с. COS3X O d.…

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Q: Find the first derivative in the form of dy/dx  y=(3x-2) sq rt(3x-2) please show all your work so…

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Q: solve the first and second derivative of Y= (1+lnx)  /  x

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: Solve differential equation by variation of parameters y"+9y = sin?(3x)

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Q: Find the given derivative. DX 5x -- Dx 5x 1/3 1/3

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Q: Va2-x² Y=Arc sin + a

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Q: find the differential equation of the family of logarithmic curves whose equation is Cy = ln(Cx).

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Q: Determine the first derivative of the ff. function a. y = 400(2)*+3 sin 3x b. y = Vxe2x cosx…

A: Given1) y=400(2)x+3sin3x2) y=xe2xcosx3)y=1+ln(3x2)1+ln(4x)We need to find the first derivative of…

Q: Find dy/dx by implicit differentiation. 3+10xv+4x-5x=0

A: Given

Q: Find dy/dx by implicit differentiation. 3x +у - 2 + х?у? У 3

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Q: 5. y = [csc Jarcsin (cos.x)

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Q: · Find dy/dx by implicit differentiation. 6. 2x? + ху — у? — 2

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Q: sin 0 · dr/d0 = -1– 2r cos 20 -1 - 2r cos 20

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Q: What is the derivative of: 4 ln(sec y + tan y) − 2x − sin 2x = 1

A: Given: 4 lnsec y+tan y-2x-sin 2x=1 To Find: dydx=?

Q: Find the seperable differential equation

A: A differential equation dydx=f(x,y) is said to be a separable equation if the given function fx,y…

Q: What is the degree of the differential equation:

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Q: y = sin(3x²) cos(3x²)

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Q: Solve the first and second derivative of y = cosh2x+ sinhx

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Q: calculate the derivative y = (sinh−1(x2))3

A: Given The chain rule of derivative is given by: The derivative of the inverse hyperbolic function…