[tex]f(x)=-e^{1-x^2}\\
f'(x)=-(-2xe^{1-x^2})\\
f'(x)=2xe^{1-x^2}\\\\
g(x)= \frac{1}{3}(e^{2x}-x)^3\\
g'(x)= \frac{1}{3}(3\times2e^{2x}-1)(e^{2x}-x)^2\\
g'(x)=(2e^{2x}- \frac{1}{3}) (e^{2x}-x)^2\\\\
h(x)= \frac{1}{(e^{3x}-e^x)^2}\\
h'(x)= \frac{-2(3e^{3x}-e^{x})}{(e^{3x}-e^x)^4}\\\\
k(x)= \sqrt{x^2+x+1}\\
k'(x)= \frac{2x+1}{2 \sqrt{x^2+x+1}} \\\\\\\\
\text{Formules utilisees}\\
f(x)=e^u \\
f'(x)=u'e^u\\\\
g(x)=ku^n\\
g'(x)=k\times n \times u' \times u^{n-1}\\\\
[/tex]
[tex]h(x)= \frac{1}{u}\\
h'(x)= \frac{-1}{u^2} \\\\
k(x)= \sqrt{u}\\
k'(x)= \frac{u'}{2 \sqrt{u} } [/tex]
