I'm sorry for this debutant question but I must ask : at 3:42, how come v = (-1/s)*e^(-st) ? I'm trying to wrap my head around the (-1/s) : for me the antiderivative of e^(-st), following the de^(u) = e^(u)*u' rule, would be -s*e^(-st).. I don't understand. Would someone be patient enough to explain it to me?
Hello! Remember that for the derivative of e^(-st), the chain rule tells us that the constant multiple "-s" would multiply the exponential. Since this is the antiderivative, the answer would have us dividing by the "-s" multiple, or you can think of it as multiplying by the reciprocal if you like. That's where we get the -1/s.
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Great examples. Thanx for covering this topic using limits! Very informative! 😊
I'm sorry for this debutant question but I must ask : at 3:42, how come v = (-1/s)*e^(-st) ? I'm trying to wrap my head around the (-1/s) : for me the antiderivative of e^(-st), following the de^(u) = e^(u)*u' rule, would be -s*e^(-st).. I don't understand. Would someone be patient enough to explain it to me?
Hello!
Remember that for the derivative of e^(-st), the chain rule tells us that the constant multiple "-s" would multiply the exponential. Since this is the antiderivative, the answer would have us dividing by the "-s" multiple, or you can think of it as multiplying by the reciprocal if you like. That's where we get the -1/s.