Wyznacz pochodne z definicji

[Gosik89]

\(\displaystyle{ e^{-x}}\)

[Crizz]

\(\displaystyle{ \left(e^{-x}\right)=\lim_{h \to 0} \frac{e^{-x-h}-e^{-x}}{h}=\lim_{h \to 0} \frac{e^{-x}(e^{-h}-1)}{h}=}\)

[yevgienij]

\(\displaystyle{ f'(x)= \lim_{h \to 0} \frac{f(x+h)-f(x)}{h}}\)

\(\displaystyle{ \lim_{h \to 0} \frac{e ^{-x-h}-e ^{-x} }{h}}\)

\(\displaystyle{ \lim_{h \to 0} \frac{e ^{-x}(e ^{-h}-1) }{h}}\)

\(\displaystyle{ \lim_{h \to 0} -e ^{-x}*( \frac{e ^{-h}-1 }{-h})}\)

\(\displaystyle{ -e ^{-x}*1=-e ^{-x}}\)