If the Laplace transform of a function f is defined and denoted by F(p), find an expression for the Laplace transform of the functions below in terms of F(p). You may assume that all necessary Laplace transforms are defined. State briefly which rule you use. h3(x) = x² f(x), h₁(x) = x f'(x).

Q: ake the derivative of this function using the power rule, product rule or quotient rule.

A: fx=3x -13xHere we can use Power Rule:ddxxn=n.xn-1

Q: Find the finite difference formula for the second derivative at point x=x; with points X₁, Xi+1,…

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Q: g(s) = (t – t3)²dt %3D

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Q: Find the derivatives of the functions in Exercis

A: we have to find the derivative of the given function. g(t)=1+sin3t3-2t-1

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. g(x) =…

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Q: Choose the derivative of sec-(æ). 1 1+ 22 1 - 1 1 V1-3 1 aVa - 1 1 1+ 22 1 1 - a2

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Q: Use the Fundamental Theorem of Calculus to find the derivative of cos t dt t8 y = [NOTE: Enter a…

A: The given function,y=∫-9xcos tt8dt