Exercise · ZW-LAPLACE-TRANSFORM-OF-A-DERIVATIVE-007 · ★★☆ Intermediate
Let \(f(t)=t^2\). Using the derivative rule with \(F(s)=2/s^3\), what is \(\mathcal L\{f'\}\)?
Choose one option.
Show answer
- D. \(\dfrac{2}{s^2}\)
Explanation
Since \(f(0)=0\), \(\mathcal L\{f'\}=s\cdot\frac2{s^3}=\frac2{s^2}\), which is \(\mathcal L\{2t\}\).
Review the concept: Laplace transform of a derivative
The Laplace transform \(\mathcal L\) of the derivative \(f'\) of a function \(f(t)\) with transform \(F(s)\) is an expression in \(F(s)\) and the initial value \(f(0)\).
\[\mathcal L\{f'\}(s)=sF(s)-f(0)\]
More practice problems: laplace transform of a derivative
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- ZW-LAPLACE-TRANSFORM-OF-A-DERIVATIVE-006 Transforming y''+4y=0, y(0)=1, y'(0)=0, what Y(s) results?
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