Exercise · ZW-LAPLACE-TRANSFORM-OF-A-DERIVATIVE-003 · ★☆☆ Basic
For \(f(t)=\sin t\) we have \(F(s)=\dfrac1{s^2+1}\) and \(f(0)=0\). What is \(\mathcal L\{f'\}\)?
Choose one option.
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- C. \(\dfrac{s}{s^2+1}\)
Explanation
Since \(f(0)=0\), \(\mathcal L\{f'\}=sF(s)=\frac{s}{s^2+1}\), the transform of \(\cos t=(\sin t)'\).
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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