Dérivée d'une fonction composée

exp(-x+2)

-exp(-x+2)

x+3

reponse

Nouvelle fonction

Valider cette réponse

Bonne réponse

Mauvaise réponse

Voir la correction proposée

(ln(x^2+4))^2

x^2+4

\left(\ln(x^2+4)\right)^2

2x

2×\frac{u'(x)}{u(x)}\ln[u(x)]

4x/(x^2+4)*ln(x^2+4)

\frac{4x}{x^2+4}\ln\left(x^2+4\right)

newfonctionfderive

newderiveTex

newfonction

newfonctionTex

newformuleDeriveTex

newuTex

\left(\ln[u(x)]\right)^2

newcomposeeTex

newderiveuTex

Ajouter

Saissisez  votre réponse ici :

\text{Calculer }f'(x)\text{ , }f'\text{ étant la fonction dérivée de la fonction }f.

RAZ

Mathématiques à Valin

Dérivée d'une fonction composée

\text{Une fois cet exercice terminé cliquez sur }
\ovalbox{\text{Envoyer et Terminer}}

Démarrer la série d'exercices

Listefonctions: {"(3x+5)^6", "sqrt(x^2+3)", "sin(3x+5)", "ln(5x^2+3)", "exp(3x+1)", "exp(-x+2)", "exp(x^2+2x-1)", "exp(cos(x))", "exp(sin(x))", "(x^3+x-1)^4", "1/(x^4+5)^3", "1/(x^2+1)^5", "((2x+1)/(x^2+1))^3", "(x/(x^2+3))^4", "ln((x^2+1)/(x^2+2))", "ln(exp(x)+3)", "ln(3*exp(x)+5)", "ln(2*exp(x)-x)", "ln(sqrt(x)+1)", "sqrt(3+sin(x))", "sqrt(3-2*cos(x))", "sqrt(x-ln(x))", "exp(3+2*cos(x))", "exp(x*sqrt(x))", "1/(2x-ln(x))", "1/(exp(x)-ln(x))", "exp(x*ln(x))", "(sin(3x+1))^3", "(cos(2x+1))^5", "x^2*exp(3x)", "x*exp(x^2+1)", "x*ln(x^2+2)", "x^2*ln(x^2+3)", "exp(3-x)/(x^2+1)", "exp(x^2-1)/(x+1)", "ln(x^2*exp(x)+1)", "(ln(x^2+4))^2"}
Listederivees: {"18*(3x+5)^5", "x/sqrt(x^2+3)", "3cos(3x + 5)", "10x/(5x^2+3)", "3*exp(3x+1)", "-exp(-x+2)", "2*(x+1)*exp(x^2+2x-1)", "-sin(x)*exp(cos(x))", "cos(x)*exp(sin(x))", "4*(3x^2+1)*(x^3+x-1)^3", "-3*(4*x^3)*(x^4+5)^(-4)", "-10x*(x^2+1)^(-6)", "(-6*(2x+1)^2*(x^2+x-1))/(x^2+1)^4", "(-4*x^3*(x^2-3))/(x^2+3)^5", "(2x)/((x^2+2)*(x^2+1))", "exp(x)/(exp(x)+3)", "3*exp(x)/(3*exp(x)+5)", "(2*exp(x)-1)/(2*exp(x)-x)", "1/(2*sqrt(x)*(sqrt(x)+1))", "cos(x)/(2*sqrt(3+sin(x)))", "2*sin(x)/(2*sqrt(3-2*cos(x)))", "(x-1)/(2x*sqrt(x-ln(x)))", "-2*sin(x)*exp(3+2*cos(x))", "1.5*sqrt(x)*exp(x*sqrt(x))", "(1-2x)/(x*(2x-ln(x))^2)", "(1-x*exp(x))/(x*(exp(x)-ln(x))^2)", "(ln(x)+1)*exp(x*ln(x))", "9*cos(3x+1)*(sin(3x+1))^2", "-10*sin(2x+1)*(cos(2x+1))^4", "x*(3x+2)*exp(3x)", "(2x^2+1)*exp(x^2+1)", "ln(x^2+2)+(2x^2)/(x^2+2)", "2x*ln(x^2+3)+(2x^3)/(x^2+3)", "-((x+1)/(x^2+1))^2*exp(3-x)", "((2x^2+2x-1)*exp(x^2-1))/(x+1)^2", "(x(x+2)*exp(x))/(x^2*exp(x)+1)", "4x/(x^2+4)*ln(x^2+4)"}
n = 6 (slider from 1 to 37, step 1)
fgh(x) = exp((-x) + 2)
ghf(x) = (-exp((-x) + 2))
ListederiveesTex: {"18(3x+5)^5", "\frac{x}{\sqrt{x^2+3}}", "3\cos(3x + 5)", "\frac{10x}{5x^2+3}", "3\text{e}^{3x+1}", "-\text{e}^{-x+2}", "2(x+1)\text{e}^{x^2+2x-1}", "-\sin(x)\text{e}^{\cos x}", "\cos(x)\text{e}^{\sin x}", "4\left(3x^2+1\right)\left(x^3+x-1\right)^3", "-\frac{12x^3}{\left(x^4+5\right)^{4}}", "-\frac{10x}{\left(x^2+1\right)^{6}}", "\frac{-6(2x+1)^2\left(x^2+x-1\right)}{\left(x^2+1\right)^{4}}", "\frac{-4x^3\left(x^2-3\right)}{\left(x^2+3\right)^{5}}", "\frac{2x}{\left(x^2+2\right)\left(x^2+1\right)}", "\frac{\text{e}^x}{\text{e}^x+3}", "\frac{3\text{e}^x}{3\text{e}^x+5}", "\frac{2\text{e}^x-1}{2\text{e}^x-x}", "\frac{1}{2\sqrt{x}\left(\sqrt{x}+1\right)}", "\frac{\cos x}{2\sqrt{3+\sin x}}", "\frac{\sin x}{\sqrt{3-2\cos x}}", "\frac{x-1}{2x\sqrt{x-\ln x}}", "-2\sin(x)\text{e}^{3+2\cos x}", "\dfrac{3}{2}\sqrt{x}×\text{e}^{x\sqrt{x}}", "\dfrac{1-2x}{x\left(2x-\ln x\right)^2}", "\dfrac{1-x\space\text{e}^x}{x\left(\text{e}^x-\ln x\right)^2}", "(1+\ln x)\text{e}^{x\ln(x)}", "9\cos(3x+1)\sin^2(3x+1)", "-10\sin(2x+1)\cos^4(2x+1)", "x(3x+2)\text{e}^{3x}", "\left(2x^2+1\right)\text{e}^{x^2+1}", "\ln\left(x^2+2\right)+\frac{2x^2}{x^2+2}", "2x\ln\left(x^2+3\right)+\frac{2x^3}{x^2+3}", "-\left(\frac{x+1}{x^2+1}\right)^2\text{e}^{3-x}", "\frac{\left(2x^2+2x-1)\text{e}^{x^2-1}}{\left(x+1\right)^2}", "\frac{x(x+2)\text{e}^x}{x^2\text{e}^x+1}", "\frac{4x}{x^2+4}\ln\left(x^2+4\right)"}
ListefonctionsTex: {"(3x+5)^6", "\sqrt{x^2+3}", "\sin(3x+5)", "\ln(5x^2+3)", "\text{e}^{3x+1}", "\text{e}^{-x+2}", "\text{e}^{x^2+2x-1}", "\text{e}^{\cos x}", "\text{e}^{\sin x}", "\left(x^3+x-1\right)^4", "\frac{1}{\left(x^4+5\right)^3}", "\frac{1}{\left(x^2+1\right)^5}", "\left(\frac{2x+1}{x^2+1}\right)^3", "\left(\frac{x}{x^2+3}\right)^4", "\ln\left(\frac{x^2+1}{x^2+2}\right)", "\ln\left(\text{e}^x+3\right)", "\ln\left(3\text{e}^x+5\right)", "\ln\left(2\text{e}^x-x\right)", "\ln\left(\sqrt{x}+1\right)", "\sqrt{3+\sin x}", "\sqrt{3-2\cos x}", "\sqrt{x-\ln x}", "\text{e}^{3+2\cos x}", "\text{e}^{x\sqrt{x}}", "\frac{1}{2x-\ln x}", "\frac{1}{\text{e}^x-\ln x}", "\text{e}^{x\ln x}", "\sin^3(3x+1)", "\cos^5(2x+1)", "x^2\text{e}^{3x}", "x\text{e}^{x^2+1}", "x\ln\left(x^2+2\right)", "x^2\ln\left(x^2+3\right)", "\frac{\text{e}^{3-x}}{x^2+1}", "\frac{\text{e}^{x^2-1}}{x+1}", "\ln\left(x^2\text{e}^x+1\right)", "\left(\ln(x^2+4)\right)^2"}
fonctionTex = Element(ListefonctionsTex, n)
deriveeTex = Element(ListederiveesTex, n)
texte1: "f(x)=" + (LaTeX[fonctionTex]) + ""
ListeuxTex: {"3x+5", "x^2+3", "3x+5", "5x^2+3", "3x+1", "-x+2", "x^2+2x-1", "\cos x", "\sin x", "x^3+x-1", "x^4+5", "x^2+1", "\frac{2x+1}{x^2+1}", "\frac{x}{x^2+3}", "\frac{x^2+1}{x^2+2}", "\text{e}^x+3", "3\text{e}^x+5", "2\text{e}^x-x", "\sqrt{x}+1", "3+\sin x", "3-2\cos x", "x-\ln x", "3+2\cos x", "x\sqrt{x}", "2x-\ln x", "\text{e}^x-\ln x", "x\ln x", "\sin(3x+1)", "\cos(2x+1)", "3x", "x^2+1", "x^2+2", "x^2+3", "3-x", "x^2-1", "x^2\text{e}^x+1", "x^2+4"}
ListederiveuTex: {"3", "2x", "3", "10x", "3", "-1", "2x+2=2(x+1)", "-\sin x", "\cos x", "3x^2+1", "4x^3", "2x", "\frac{-2\left(x^2+x-1\right)}{\left(x^2+1\right)^2}", "\frac{\left(-x^2+3\right)}{\left(x^2+3\right)^2}", "\frac{2x}{\left(x^2+2\right)^2}", "\text{e}^x", "3\text{e}^x", "2\text{e}^x-1", "\frac{1}{2\sqrt{x}}", "\cos x", "2\sin x", "\frac{x-1}{x}", "-2\sin x", "\dfrac{3}{2}\sqrt{x}", "\dfrac{2x-1}{x}", "\text{e}^x-\frac{1}{x}", "\ln x+1", "3\cos(3x+1)", "-2\sin(2x+1)", "3", "2x", "2x", "2x", "-1", "2x", "x(x+2)\text{e}^x", "2x"}
ChampTexte1 = Textfield(textrepbrut)
k(x) = x + 3
h = If(Defined[k], k, x + 100)
texteh = LaTeX(h, true, false)
texthfinal = If(Defined[k], texteh, "")
texte3: "f'(x)=" + (LaTeX[texthfinal]) + ""
bonnereponse: h(1.3) ≟ ghf(1.3) ∧ h(1.5) ≟ ghf(1.5) ∧ h(1.9) ≟ ghf(1.9) ∧ h(1.7) ≟ ghf(1.7)
textu = Element(ListeuxTex, n)
textderiveu = Element(ListederiveuTex, n)
ListeCompose: {"[u(x)]^6", "\sqrt{u(x)}", "\sin(u(x))", "\ln[u(x)]", "\text{e}^{u(x)}", "\text{e}^{u(x)}", "\text{e}^{u(x)}", "\text{e}^{u(x)}", "\text{e}^{u(x)}", "[u(x)]^4", "[u(x)]^{-3}", "[u(x)]^{-5}", "[u(x)]^{3}", "[u(x)]^{4}", "\ln [u(x)]", "\ln [u(x)]", "\ln [u(x)]", "\ln [u(x)]", "\ln [u(x)]", "\sqrt{u(x)}", "\sqrt{u(x)}", "\sqrt{u(x)}", "\text{e}^{u(x)}", "\text{e}^{u(x)}", "\frac{1}{u(x)}", "\frac{1}{u(x)}", "\text{e}^{u(x)}", "[u(x)]^3", "[u(x)]^5", "x^2\text{e}^{u(x)}", "x\text{e}^{u(x)}", "x\ln[u(x)]", "x^2\ln[u(x)]", "\frac{\text{e}^{u(x)}}{x^2+1}", "\frac{\text{e}^{u(x)}}{x+1}", "\ln[u(x)]", "\left(\ln[u(x)]\right)^2"}
composee = Element(ListeCompose, n)
listeformules: {"6u'(x)[u(x)]^5", "\frac{u'(x)}{2\sqrt{u(x)}}", "u'(x)\cos[u(x))]", "\frac{u'(x)}{u(x)}", "u'(x)\text{e}^{u(x)}", "u'(x)\text{e}^{u(x)}", "u'(x)\text{e}^{u(x)}", "u'(x)\text{e}^{u(x)}", "u'(x)\text{e}^{u(x)}", "4u'(x)[u(x)]^3", "-3u'(x)[u(x)]^{-4}", "-5u'(x)[u(x)]^{-6}", "3u'(x)[u(x)]^{2}", "4u'(x)[u(x)]^{3}", "\frac{u'(x)}{u(x)}", "\frac{u'(x)}{u(x)}", "\frac{u'(x)}{u(x)}", "\frac{u'(x)}{u(x)}", "\frac{u'(x)}{u(x)}", "\frac{u'(x)}{2\sqrt{u(x)}}", "\frac{u'(x)}{2\sqrt{u(x)}}", "\frac{u'(x)}{2\sqrt{u(x)}}", "u'(x)\text{e}^{u(x)}", "u'(x)\text{e}^{u(x)}", "-\frac{u'(x)}{[u(x)]^2}", "-\frac{u'(x)}{[u(x)]^2}", "u'(x)\text{e}^{u(x)}", "3u'(x)[u(x)]^2", "5u'(x)[u(x)]^4", "2x\text{e}^{u(x)}+x^2u'(x)\text{e}^{u(x)}", "\text{e}^{u(x)}+x× u'(x)\text{e}^{u(x)}", "\ln[u(x)]+x× \frac{u'(x)}{u(x)}", "2x×\ln[u(x)]+x^2× \frac{u'(x)}{u(x)}", "\frac{u'(x)\text{e}^{u(x)}\left(x^2+1\right)-2x\text{e}^{u(x)}}{\left(x^2+1\right)^2}", "\frac{u'(x)\text{e}^{u(x)}\left(x+1\right)-\text{e}^{u(x)}}{\left(x+1\right)^2}", "\frac{u'(x)}{u(x)}", "2×\frac{u'(x)}{u(x)}\ln[u(x)]"}
formule = Element(listeformules, n)
texte2: "\text{or  }f'(x)=" + (LaTeX[formule]) + "\text{   donc   }f'(x)=" + (LaTeX[deriveeTex]) + ""
voirréponse = false
test = false
ChampTexte2 = Textfield(newderive)
ChampTexte3 = Textfield(newderiveTex)
ChampTexte4 = Textfield(newfonction)
ChampTexte5 = Textfield(newfonctionTex)
ChampTexte6 = Textfield(newformule)
ChampTexte7 = Textfield(newu)
ChampTexte8 = Textfield(newcomposee)
ChampTexte9 = Textfield(newuTex)
texte7: "" + (LaTeX[newfonctionTex]) + ""
texte8: "" + (LaTeX[newuTex]) + ""
texte9: "" + (LaTeX[newu]) + ""
texte10: "" + (LaTeX[newderiveTex]) + ""
voirconstruction = false
debut = false
decale = 17
score = 0
nbexo = 1
gain = 1
texte13: "Nombre d'exercices réussis : " + score + " sur " + nbexo + " proposés"
grade: score
texte4: "\text{Si on pose  } u(x)=" + (LaTeX[textu]) + "\text{    alors    }f(x)=" + (LaTeX[composee]) + "\text{    et   } u'(x)=" + (LaTeX[textderiveu]) + "\\
\phantom{.}\\" + (LaTeX[texte2]) + ""
notemax: 10