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Differentiation of e^x

Doc Boff Maths AS level Inglés 8 fichas

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1e = ......2.718......
2y=e^x can be defined by....1 + x + x^2/2! + x^3/3! + x^4/4! + ... (infinite)
(don't need to know necessarily)
3dy/dx of y=e^x can be defined by....0 + 1 + 2x/2! + 3x^2/3! + 4x^3/4! + ...(infinite)
(don't need to know necessarily)
40 + 1 + 2x/2! + 3x^2/3! + 4x^3/4! + ... cancels to.....1 + x + x^2/2! + x^3/3! + x^4/4! + ...
(don't need to know necessarily)
5Therefore dy/dx of y=e^x and y=e^x itself give....The same (e^x)
(need to know)
6If y=5e^x , dy/dx = .....5e^x
7If y=e^2x , dy/dx = .....2e^2x
8If y=Ae^kx , dy/dx = .....Ake^kx