Derivate
Calcolare le derivate delle seguenti funzioni
1. y= 3x2−2x+3
√x y0= 6x−2 + 1
33
√x2
2. y=x−1
x+2 y0=3
(x+2)2
3. y=ex
ex+1 y0=ex
(ex+1)2
4. y=exsin x
excos x+1 y0=ex(1+sin x+cos x)
(excos x+1)2
5. y= (x2−2) sin x y0= 2xsin x+ (x2−2) cos x
6. y=ln x
3 ln x−2y0=−2
x(3 ln x−2)2
7. y=x2ex
x−1y0=xex(x2−2)
(x−1)2
8. y=ex
·sin x·ln x·x2y0=xex(xln x(sin x+ cos x) + sin x(1 + 2 lnx))
Calcolare le derivate delle seguenti funzioni (funzioni inverse e composte)
1. y=√x2−5x+ 1 y0=2x−5
2√x2−5x+1
2. y= (cos x)3y0=−3 sin x(cos x)2
3. y=√ln x y0=1
2x√ln x
4. y= sin(x3−2x)y0= (3x2−2) cos(x3−2x)
5. y= (ln(x2−5))5y0=10x
x2−5(ln(x2−5))4
6. y= arcsin(x2)y0=2x
√1−x4
7. y=e−x2
−1
xy0=−
x2+1
x2e−x2
−1
x
8. y=xsin xy0=xsin xcos xln x+sin x
x
9. y= ln arctan x−1
x+2 y0=3
(2x2+2x+5) arctan x−1
x+2
10. y=esin ln(x2+2) y0=esin ln(x2+2) ·cos ln(x2+ 2) ·2x
x2+2
1
ex
