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last edited on October 29, 2008 11:43 AM by admin

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diff(sin(5*x),x) 5*cos(5*x) diff(x^2*sin(3*x),x) 2*x*sin(3*x) + 3*x^2*cos(3*x) diff(sin(2*x^3-1)^2,x) 12*x^2*cos(2*x^3 - 1)*sin(2*x^3 - 1) diff(sqrt(1+cos(x)^3),x) -3*cos(x)^2*sin(x)/(2*sqrt(cos(x)^3 + 1)) diff(cos(2*x^4-3*x^2+1)^5,x) -5*(8*x^3 - 6*x)*cos(2*x^4 - 3*x^2 + 1)^4*sin(2*x^4 - 3*x^2 + 1) diff(x^2*sin(1/x^2),x) 2*sin(1/x^2)*x - 2*cos(1/x^2)/x diff(3^(sin(x)/x),x) log(3)*(cos(x)/x - sin(x)/x^2)*3^(sin(x)/x) #Exo2 diff(log(1+x^2),x) 2*x/(x^2 + 1) diff(log(log(x)),x) 1/(x*log(x)) diff(2^(x^2),x) 2*log(2)*x*2^x^2 diff(x^x,x) x^x*(log(x) + 1) diff(exp(2*x)*log(3*x),x) 2*e^(2*x)*log(3*x) + e^(2*x)/x diff(x^(log(2*x)),x) x^log(2*x)*(log(2*x)/x + log(x)/x) #Exo 3 #Rappel : diff(arctan(x),x) 1/(x^2 + 1) f=arctan(sqrt(1-cos(x))/sqrt(1+cos(x))) print f sqrt(1 - cos(x)) arctan(----------------) sqrt(cos(x) + 1) g=f.diff(x) print g sin(x) sqrt(1 - cos(x)) sin(x) ----------------------------------- + ----------------------2 sqrt(1 - cos(x)) sqrt(cos(x) + 1) 3/2 2 (cos(x) + 1) ------------------------------------------------------------1 - cos(x) ---------- + 1 cos(x) + 1

plot(g(x),x,[-10,10])

#Exo 4 f4=1/3*sqrt(36-4*x^2) print f4 2 sqrt(36 - 4 x ) --------------3 g4=f4.diff(x) print g4 print (g4(sqrt(5))) plot (g4,[-3,3]) 4 x - ----------------2 3 sqrt(36 - 4 x ) sqrt(5) - ------3

#Exo 5 f5=sqrt(sqrt(1+x^2)-x) g5=f5.diff(x) print g5 print g5(0) plot (g5,[-10,10]) x ------------ - 1 2 sqrt(x + 1) -----------------------2 2 sqrt(sqrt(x + 1) - x) 1 - 2

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