Per esercitarsi sulle derivate

Pierre Auguste Renoir

Si calcolino le derivate prime delle seguenti funzioni ed il relativo dominio.

 

 

Per un livello sufficiente (6)

6.1 y=2x+5 \left [y^{'}=2  \right ]
6.2.  y=4x^{2} \left [y^{'}=8x  \right ]

Per un livello discreto (7)

 7.1.  y=\cfrac{1}{x}.  \left [y^{'}=-\cfrac{1}{x^2}  \right ]

4) y=\sqrt{x+5}.

5) y=(1+x)^{2}.

6) y=4ln(x)-e^{x}+2x^{4}.

7) y=ln(x)+2\sqrt{x}.

8) y=4x^{3}+2x^{2}-3x+5.

9) y=x^{2}\cdot e^{x}.

10) y=2x^{2}\cdot ln(x).

11) y=(3x+5)\cdot e^{x}.

12) y=5\cdot e^{x}\cdot ln(x).

13) y=\cfrac{x+3}{2x}.

14) y=\cfrac{x}{x^{2}+3}.

15) y=\cfrac{x^{2}+5}{x-1}.

16) y=\cfrac{x-4}{x^{2}-2}.

17) y=\cfrac{x^{2}+x+1}{2x-x^{2}}.

18) y=\cfrac{e^{x}}{x}.

19) y=(2x+4)^{3}.

20) y=\cfrac{1}{(x^{2}+2)^{2}}.

21) y=ln(\sqrt{x}).

22) y=3\cdot e^{2x+5}.

23) y=\sqrt{\cfrac{3x}{x+1}}.

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One Response to Per esercitarsi sulle derivate

  1. Francesco Bragadin says:

    Per l’esercizio 1 qual è il dominio?

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