6.2 Transforms of derivatives and ODEs: Problem 1 (20 points) Consider the following initial value problem: x" -5x-24x=sin(2t), x(0) = 1, x'(0) = = −4. Using X for the Laplace transform of x(t), i.e., X = L{x(t)}, find the equation you get by taking the Laplace transform of the differential equation and solve for X(s) = ☐ help (formulas) Book: Section 6.2 of Notes on Diffy Qs

Q: 3 (8) Consider the curve given by 23 + x?y+ y³ = 1 Use implicit differentiation to find the equation…

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Q: 4 (6) Find the derivative y' for the Following function 2x 1) Y = √₂²² sin (e²-1)dt 2y=1-cos (x ²-2)…

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Q: If u = and , then what is the magnitude of 2 + . Round to the nearest hundredth. Answer:

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Q: Homework: (1) Using the definition of derivative, find the derivative of the following functions:…

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Q: g(0)=sin 0:

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Q: - 1. Find the first derivative of the function S(x)=x² sec ) completely and simplify your answer.

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Q: 1 Find the derivative of g(x)= (x)sec(x) + a+ x* + cos - sin(x)

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Q: Determine the derivative of y=| 3e2x with respect to x ((x+1) (Inex² O Integrato the fo IL

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Q: Find the derivative of this complex equation using logarithmic differentiation?

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Q: 3 | (x + 7)10(5x − 1) (8x + 8)² Use logarithmic differentiation to find the derivative of f. Let…

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Q: Example 7: Find all of the second derivatives for f (x, y) = 3xy2 + 2xy + x2. %3D

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Q: If y = sin (4x - 5), then what is y' a. y = 4 cos (4x - 5) b. y 3 сos (4x - 5) C. y' = -cos (4x) d.…

A: In this question  we have to solve the given statements. NOTE: As per our policy we are suppose to…

Q: 8-1. 8-2. Find a general form anti-derivative for the following functions: (a) f(r) = 722/5 + 8z-4/5…

A: we have to find the antiderivative of g(x)

Q: Find the derivative of the function. h(e)- (-1) ( 1) +]

A: Given ht=t4-15t3+16

Q: a) Using the definition of derivative, calculate the derivative of the function of f(x) = /3x +1 (b)…

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Q: 8. Given that f(x) =1+vx² + 3x + 6 find f'(2).

A: The derivative of the function fx at x=a is defined as follows: f'a=limh→0fa+h-fah

Q: 17) Find the derivative of y = x? COs x - 2

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Q: What is the purpose of implicit differentiation? To find dy/dx without having to solve for y To find…

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Q: Consider y = (1 + 3x²) Arctan x - 3. what is its derivative? %3D 1 +3x2 1 + x2 A - 6x Arctan x 1…

A: 7). As we know that: The product rule:  f·g'=f'·g+f·g' The sum/difference rule: f±g'=f'±g' The Power…

Q: Given the following function S (x)= ax' +bx² +cx+d where а -1 b- 82 c-7 d-0 The step size for h is…

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Q: Question No 1: Using the quotient rule to differentiate the x3+1 following function y = Vx2+1

A: As per our company guidelines, we are supposed to answer only the first question. Kindly repost…

Q: Use the following information to solve the first two questions. Gamma function r(a)=√₁²-¹. e In…

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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: Problem 2 Find dy/dx of y = x* at the point (2,4) by following a similar procedure: 1. Apply In() to…

A: Applying “ln” on both sides of equation and simplifying.