Página 115

15. y=(x^2) * log (x^2);

>> diff(y)

ans =

2*x + 2*x*log(x^2)

16. y=e^(n*x);

diff(y,x)

ans =

n*e^(n*x)

17. y=10^(n*x);

>> diff(y,x)

ans =

10^(n*x)*n*log(10)

18. y=e^(x^2);

>> diff(y,x)

ans =

2*e^(x^2)*x

19. y=2/e^x;

>> diff(y,x)

ans =

-2/e^x

20. s=e^(sqrt(t));

>> diff(s,t)

ans =

(e^(t^(1/2)))/(2*t^(1/2))

Página 116

21. z=b^(2*y);

>> diff(z,y)

ans =

2*b^(2*y)*log(b)

22. u=s*e^s;

>> diff(u,s)

ans =

e^s + e^s*s

23. v=(e^u)/u;

>> diff(v,u)

ans =

e^u/u - e^u/u^2

24. y=(log x)/x;

>> diff(y)

ans =

(1- log x)/x^2

25. y=log ((x^2)*e^x);

>> diff(y,x)

ans =

(2*e^x*x + e^x*x^2*log(e))/(e^x*x^2)

26. y=(e^x -1)/(e^x +1);

>> diff(y,x)

ans =

(e^x)/(e^x + 1) - (e^x*(e^x - 1))/(e^x + 1)^2

27. y=(x^2)*e^-x;

>> diff(y,x)

ans =

(2*x)/e^x - (x^2)/e^x

28. y=(a/2)*(e^(x/a) - e^(-x/a));

diff(y,x)

ans =

1/(2*e^(x/a)) + (e^(x/a))/2

29. y=(e^x -e^-x)/(e^x +e^-x);

>> diff(y,x)

ans =

(e^x + 1/e^x)/(e^x + 1/e^x) - ((e^x - 1/e^x)*(e^x - 1/e^x))/(e^x + 1/e^x)^2

30. s=(log t^2)/t^2;

>> diff(s,t)

ans =

(2 – 4* log (t))/t^3

31. f=log (sqrt(x^2 +1)-x)/(sqrt(x^2 +1)+x);

>> diff(f)

ans =

- (x/(x^2 + 1)^(1/2) - 1)/((x + (x^2 + 1)^(1/2))*(x - (x^2 + 1)^(1/2))) - ((x^2 + 1)^(1/2) - x)*(x/(x^2 +

1)^(1/2) + 1))/(x + (x^2 + 1)^(1/2))^2

32. y=x^x;

>> diff(y)

ans =

x*x^(x - 1) + x^x*log(x)

33. y=x^sqrt(x);

>> diff(y)

ans =

x^(1/2)*x^(x^(1/2) - 1) + (x^(x^(1/2))*log(x))/(2*x^(1/2))