Practice Derivative Theorem (15.7.3) - Fourier Integral to Laplace Transforms
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Derivative Theorem

Practice - Derivative Theorem

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Practice Questions

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Question 1 Easy

What does the Derivative Theorem allow you to do with derivatives of a function in Laplace transforms?

💡 Hint: Think about how we handle initial values.

Question 2 Easy

Use the Derivative Theorem to find the Laplace transform of the equation y' + 4y = 0 with y(0) = 3.

💡 Hint: Apply the theorem then substitute the initial conditions.

1 more question available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the Derivative Theorem express for the Laplace transform of a derivative?

It expresses it as F(s).
It expresses it as a function of s only.
It relates it to initial conditions and F(s).

💡 Hint: Think about what initial conditions the theorem considers.

Question 2

True or False: The Derivative Theorem is not required for solving initial value problems.

True
False

💡 Hint: Consider its application in ODEs.

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Challenge Problems

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Challenge 1 Hard

For the function f(t) = e^{-t}, calculate L{f''(t)} using the Derivative Theorem and given f(0) = 1 and f'(0) = -1.

💡 Hint: Start by finding F(s) before computing the derivatives.

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