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Let-f-x-0-x-e-t-dt-then-f-x-




Question Number 110247 by Rio Michael last updated on 28/Aug/20
Let f(x) = ∫_0 ^( x) e^(−t) dt   then f ′′(x) = ??
$$\mathrm{Let}\:{f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\:{x}} {e}^{−{t}} {dt}\: \\ $$$$\mathrm{then}\:{f}\:''\left({x}\right)\:=\:?? \\ $$
Answered by bemath last updated on 28/Aug/20
f ′(x)=e^(−x)  ⇒f ′′(x)=−e^(−x)
$${f}\:'\left({x}\right)={e}^{−{x}} \:\Rightarrow{f}\:''\left({x}\right)=−{e}^{−{x}} \\ $$

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