{"type":"rich","version":"1.0","title":"Deriving the derivative rule of the Laplace transform by integration by parts","html":"<span class=\"wb-embed wb-embed-math\" data-latex=\"\\mathcal{L}\\{f'\\}=\\int_{0}^{\\infty}e^{-st}f'(t)\\,dt=\\bigl[e^{-st}f(t)\\bigr]_{0}^{\\infty}+s\\int_{0}^{\\infty}e^{-st}f(t)\\,dt=sF(s)-f(0)\">\\mathcal{L}\\{f'\\}=\\int_{0}^{\\infty}e^{-st}f'(t)\\,dt=\\bigl[e^{-st}f(t)\\bigr]_{0}^{\\infty}+s\\int_{0}^{\\infty}e^{-st}f(t)\\,dt=sF(s)-f(0)</span>","width":640,"height":320}