The document contains 33 math problems involving derivatives. For each problem, the function is defined, the derivative is taken, and the result is displayed. The problems cover a range of standard functions including exponentials, logarithms, and combinations of functions.

1. 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))

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;

3. >> 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)

4. ans =
x^(1/2)*x^(x^(1/2) - 1) + (x^(x^(1/2))*log(x))/(2*x^(1/2))