diff --git a/test/exercice - calculs de derivee - 2020.1.fodt b/test/exercice - calculs de derivee - 2020.1.fodt new file mode 100644 index 0000000..4cd1e98 --- /dev/null +++ b/test/exercice - calculs de derivee - 2020.1.fodt @@ -0,0 +1,5971 @@ + + + + 2016-03-22T17:15:32.5124790002020-11-01T21:31:55.108764988PT3H33M33S50LibreOffice/7.4.7.2$Linux_X86_64 LibreOffice_project/40$Build-2Jean-François LANCEJean-François LANCE2020-10-27T16:14:35.192336331 + + + 0 + 0 + 30496 + 13612 + true + false + + + view2 + 5447 + 1201 + 0 + 0 + 30494 + 13610 + 0 + 1 + false + 160 + false + false + true + + + + + false + false + false + true + true + true + true + true + false + 0 + false + false + false + false + true + false + true + false + false + false + false + true + true + true + false + false + false + false + false + false + false + false + true + false + false + true + false + false + false + true + 0 + 1 + true + false + + high-resolution + true + + 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10§display§\mathbb{R}§svg§600§TRUE§ + + + + + et on a + TexMaths + 10§display§u'(x) = 2x§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + et + TexMaths + 10§display§v'(x) = 1§svg§600§TRUE§ + + + + + + + + + + + + + + + + + . + + Donc + TexMaths + 10§display§f§svg§600§TRUE§ + + + + + est dérivable sur + TexMaths + 10§display§\mathbb{R}§svg§600§TRUE§ + + + + + et + TexMaths + 10§display§f'(x) = 2x + 1§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + . + + + + + Pour chacune des fonctions + TexMaths + 10§display§f§svg§600§TRUE§ + + + + + suivantes, donner son ensemble de définition, celui de sa dérivée et l'expression de sa dérivée, + TexMaths + 10§display§f'§svg§600§TRUE§ + + + + + + +  : + + + + + + + + + + a) + + + + TexMaths + 10§display§f(x) = x^2 + 5§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + + d) + + + + TexMaths + 10§display§f(x) = 2x + \dfrac{1}{x}§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + + + + + + g) + + + + TexMaths + 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+ + Pour chacune des fonctions + TexMaths + 10§display§f§svg§600§TRUE§ + + + + + suivantes, donner son ensemble de définition, celui de sa dérivée et l'expression de sa dérivée, + TexMaths + 10§display§f'§svg§600§TRUE§ + + + + + + +  : + + + + + + + + + + a) + + + + TexMaths + 10§display§f(x) = 3\sqrt{x}§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + + c) + + + + TexMaths + 10§display§f(x) = 5x^5 - 3x^2§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + e) + + + + TexMaths + 13§display§f(x) = 7e^x§svg§600§TRUE§ + + PD94bWwgdmVyc2lvbj0nMS4wJyBlbmNvZGluZz0nVVRGLTgnPz4KPCEtLSBUaGlzIGZpbGUg + d2FzIGdlbmVyYXRlZCBieSBkdmlzdmdtIDIuNi4xIC0tPgo8c3ZnIGhlaWdodD0nOS45NjI2 + NHB0JyB2ZXJzaW9uPScxLjEnIHZpZXdCb3g9Jzc2LjcxMjMyOSA1NS4yOTI2NTMgNDYuODE0 + MDUxIDkuOTYyNjQnIHdpZHRoPSc0Ni44MTQwNTFwdCcgeG1sbnM9J2h0dHA6Ly93d3cudzMu + b3JnLzIwMDAvc3ZnJyB4bWxuczp4bGluaz0naHR0cDovL3d3dy53My5vcmcvMTk5OS94bGlu + 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FqJWkftPFg59+/bt36ampvqDLAIa1JPKIGjOh2qUsYsXL27mJ20tEfmRigdClhapy5Yt+yUh + ISFY+CYS+MlSkrQGt1DOPa+hkoQ0KimVItyPhHdra+t6Re4rS0Apv8ntEHVgYGCyvOuIiDDy + JLUxN2xJg/AyN1cuSvJGGhexffv2fSGvIv/LuDMo+6jH4QNZ1Q0pinTERUVWRYDAHfw9MH/+ + /N8Vr/K/V/4GW3+Coz13/QYAAAAASUVORK5CYII= + + + + + + + + + + … dériver un produit de fonctions + + + + + Exemple : Soit + TexMaths + 10§display§f§svg§600§TRUE§ + + + + + définie sur + TexMaths + 10§display§\mathbb{R}^{+}§svg§600§TRUE§ + + + + + + + par + TexMaths + 10§display§f(x) = (4x^2 - 3x)\sqrt{x}§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + . + + On pose + TexMaths + 10§display§u(x) = 4x^2 - 3x§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + + + et + TexMaths + 10§display§v(x) = \sqrt{x}§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + . + + La fonction + TexMaths + 10§display§u§svg§600§TRUE§ + + + + + est définie et dérivables sur + TexMaths + 13§display§\mathbb{R}§svg§600§TRUE§ + + 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On a + TexMaths + 10§display§u'(x) = 8x - 3§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + . + La fonction + TexMaths + 13§display§v§svg§600§TRUE§ + + PD94bWwgdmVyc2lvbj0nMS4wJyBlbmNvZGluZz0nVVRGLTgnPz4KPCEtLSBUaGlzIGZpbGUg + d2FzIGdlbmVyYXRlZCBieSBkdmlzdmdtIDIuNi4xIC0tPgo8c3ZnIGhlaWdodD0nNC4yODk0 + NjhwdCcgdmVyc2lvbj0nMS4xJyB2aWV3Qm94PSc3Ni43MTIzMjkgNTguNDc1MTY1IDUuMTg2 + NTgyIDQuMjg5NDY4JyB3aWR0aD0nNS4xODY1ODJwdCcgeG1sbnM9J2h0dHA6Ly93d3cudzMu + b3JnLzIwMDAvc3ZnJyB4bWxuczp4bGluaz0naHR0cDovL3d3dy53My5vcmcvMTk5OS94bGlu + ayc+CjxyZWN0IGZpbGw9IiNmZmZmZmYiIHg9Ijc2LjcxMjMyOSIgeT0iNTguNDc1MTY1IiB3 + aWR0aD0iNS4xODY1ODIiIGhlaWdodD0iNC4yODk0NjgiIHN0eWxlPSJmaWxsLW9wYWNpdHk6 + MCIvPgo8ZGVmcy8+CjxnIGlkPSdwYWdlMSc+CjxwYXRoIGQ9J004MS4zNzQ4NDQgNTkuMDU4 + NTMxQzgxLjM3NDg0NCA1OC41MjA1NDggODEuMTE1ODE2IDU4LjM2MTE0NiA4MC45MzY0ODgg + NTguMzYxMTQ2QzgwLjY4NzQyMiA1OC4zNjExNDYgODAuNDQ4MzE5IDU4LjYyMDE3NCA4MC40 + NDgzMTkgNTguODM5MzUyQzgwLjQ0ODMxOSA1OC45Njg4NjcgODAuNDk4MTMyIDU5LjAyODY0 + 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1LxxKxv5fwXi7IqKCn88jCCGnpqa0oXzweM36v8GRK/TDLa4vEMAAAAASUVORK5CYII= + + + + + + + + + + + + + + + + … dériver un quotient de fonctions + + + + + Exemple : Soit + TexMaths + 10§display§f§svg§600§TRUE§ + + + + + définie sur + TexMaths + 10§display§\mathbb{R}§svg§600§TRUE§ + + + + + par + TexMaths + 10§display§f(x) = \dfrac{-3x + 5}{x^2 + 1}§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + . + + On pose + TexMaths + 10§display§u(x) = -3x + 5§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + et + TexMaths + 10§display§v(x) = x^2 + 1§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + . + + Les fonctions + TexMaths + 10§display§u§svg§600§TRUE§ + + + + + et + TexMaths + 10§display§v§svg§600§TRUE§ + + + + + sont définies et dérivables sur + TexMaths + 10§display§\mathbb{R}§svg§600§TRUE§ + + + + + . + TexMaths + 13§display§v§svg§600§TRUE§ + + PD94bWwgdmVyc2lvbj0nMS4wJyBlbmNvZGluZz0nVVRGLTgnPz4KPCEtLSBUaGlzIGZpbGUg + 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+ TexMaths + 10§display§f'(x) = \dfrac{u'(x) \times v(x) - u(x) \times v'(x)}{v^2(x)} + += \dfrac{-3 \times (x^2+1) - (-3x+5) \times 2x}{(x^2+1)^2} + += \dfrac{3x^2 - 10x - 3}{x^4 + 2x^2 + 1}§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + . + + + + + Pour chacune des fonctions + TexMaths + 10§display§f§svg§600§TRUE§ + + + + + suivantes, donner son ensemble de définition, celui de sa dérivée et l'expression de sa dérivée, + TexMaths + 10§display§f'§svg§600§TRUE§ + + + + + + +  : + + + + + + + + + + a) + + + + TexMaths + 10§display§f(x) = \dfrac{x+2}{2x-3}§svg§600§TRUE§ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + d) + + + + TexMaths + 13§display§f(x) = 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