Réponse : Bonjour,
[tex]\frac{dy}{dx}=3\left(\frac{5x^{4}}{2\sqrt{x^{5}}}\right)=\frac{15x^{4}}{2\sqrt{x^{5}}}[/tex].
[tex]\frac{d^{2}y}{dx^{2}}=3\left(\frac{5 \times 4x^{3} \times 2\sqrt{x^{5}}-2 \times \frac{5x^{4}}{\sqrt{x^{5}}}\times 5x^{4}}{(2\sqrt{x^{5}})^{2}}\right)=3\left(\frac{40x^{3}\sqrt{x^{5}}-\frac{50x^{8}}{\sqrt{x^{5}}}}{4x^{5}}\right)\\=3\left(\frac{\frac{40x^{3}x^{5}-50x^{8}}{\sqrt{x^{5}}}}{4x^{5}}\right)=3\left(\frac{\frac{-10x^{8}}{\sqrt{x^{5}}}}{4x^{5}}\right)=3\frac{-10x^{8}}{4x^{5}\sqrt{x^{5}}}=-\frac{30x^{8}}{4(x^{5})^{\frac{3}{2}}}[/tex]
