Practice Proof of First Derivative - 1.1.4 | 5. Laplace Transform of Derivatives | Mathematics - iii (Differential Calculus) - Vol 1
Students

Academic Programs

AI-powered learning for grades 8-12, aligned with major curricula

Engineering Courses
Professional

Professional Courses

Industry-relevant training in Business, Technology, and Design

Certifications
Games

Interactive Games

Fun games to boost memory, math, typing, and English skills

Proof of First Derivative

1.1.4 - Proof of First Derivative

Enroll to start learning

You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the Laplace Transform of f(t) = t?

💡 Hint: Use the basic formula of Laplace Transform.

Question 2 Easy

Write the formula for L{f'(t)}.

💡 Hint: Recall the transformation equation discussed.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the Laplace Transform of f'(t)?

sF(s) + f(0)
sF(s) - f(0)
0

💡 Hint: Remind yourself of the transformation formulas.

Question 2

True or False: The Laplace Transform can only be used for first derivatives.

True
False

💡 Hint: Think about the different orders of derivatives we've covered.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given f(t) = e^{at} sin(bt), find the Laplace Transform using properties of derivatives implicitly.

💡 Hint: Use the formula for the Laplace Transform of functions multiplied by an exponential.

Challenge 2 Hard

Prove the formula for L{f(n)(t)} = s^nF(s) - Σ from k=0 to n-1 of s^{n-1-k} f^(k)(0).

💡 Hint: Work step-by-step through the integrations as shown in the previous examples.

Get performance evaluation

Reference links

Supplementary resources to enhance your learning experience.