Question 86 Apply the Laplace transform to resolve th y"= 5g²-6y=0 y (0) Initially, denote the Laplace transform of Y= L {y (t)} Then, ascertain the equation derived by a the differential equation. =0 Know this now solve for Y(s)=_

Q: What is the derivative of y= 3Arcsin xº, 3 Arcsin x In 3 A y' = 1 - xa 3 Arcsin x* In 3 3 B y' : (а…

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Q: dy 13. Find the derivative, dx' x³y? = In(xy²) – 7x2

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Q: 3x y=3- + Arccos V8-x3

A: We have to find out the first derivative  .

Q: Find the derivative of the function. y = In (7+x²) O XIN 14

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Q: Find the derivative of g(x) = e * x). sin (1+ 0-3x²e*cos(1+x°) O xe*1sin(1+x°)+3x²e*cos(1+x) O…

A: The product rule of derivatives states that duv=u'v+v'u.

Q: Find the equation of the tangent line of f(x) = 8/x+3 at the point (4, 19) . Express your answer in…

A: Find the equation of the tangent line of fx=8x+3 at the pint (4,19).

Q: (8) Find the differential for the function using logarithmic differentiation. y = (sin x) (sec): dy…

A: The given function is .The aim is to find the differential for the given function.Formula used:

Q: If H (x) = x² (2x-41)

A: H(x)=x2(2x−11−4x)

Q: . Find L(t cos at } .

A: We will be using the known formulas to arrive at the final answer.

Q: sinh (u+v)=sinhycoshr+ coshuxsinhv

A: Use hyperbolic function

Q: QUESTION 5 Find the derivative. y%3= + 8 sec x Oy'-2- 8 sec x tan x x2 Oy'- - 7. +8 sec x tan x Oy'=…

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Q: Determine the solution of the differential equation shown using Laplace and Inverse Laplace…

A: Given y'''−y=4e−x+3e2x.....1 When, x=0, y=0, y'=−1 and y''=2 Take Laplace transformation of equation…

Q: Find the given higher-order derivative. 1. f'(x) = 5x? f''(x) = 2. f''(x) = 5 – - f"(#) = 3. f'(x) =…

A: Note: As per company guidelines we are supposed to solve only 1 question or 3 subaprts. So, kindly…

Q: Find the derivative of the function f(x) = Jet – In(/x) (e+12 – 1) O (e:/2 – 1/x)

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Q: Determine the differential operators of the following: 1. Solve (e sinx) using exponential shift

A: Given,  d2dx2e3xsinx Thus, the differential operator is p(D)=D2=d2dx2. To solve the d2dx2e3xsinx by…

Q: Calculate two iterations of Newton's Method to approximate a zero of the function using the given…

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Q: show that if y=x/tan(x) then y'=cot(x)-csc(x)

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Q: If f(x)=√x+3, g(x)=x², then (fog)(x) = The differential of the function f(x)=tan(cos.x) is_ The…

A: We know that derivative of d(cosx)/dx = -sinx. And d(tanx)/dx = sec2x. And derivatives power rule is…

Q: We let u = 1+cos^2x, the take the derivative. The derivative is du=2(cos(x))(-sin(x))dx. Then it…

A: our objective is to understand what's happening

Q: Find the derivative: 2 (2 + y) = y? O y = y(2-y) z(1+2) z(2z+y) y(1-2) Oy = 2+) z(1-2) y(22+) |3D Oy…

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Q: Consider the differential equation y=-2x (A) At the point (1, -1), the direction field has a slope…

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