MATEMATICA

1. ---------------------------------------DERIVADAS-------------------------------------------------
1)
>> syms x;
>> y=(2*x+3)/(3*x-2);
>> diff(y)
ans =
2/(3*x-2)-3*(2*x+3)/(3*x-2)^2
>> 2/(3*x-2)-3*(2*x+3)/(3*x-2)^2
ans =
2/(3*x-2)-(6*x+9)/(3*x-2)^2
>> a=2/(3*x-2)-(6*x+9)/(3*x-2)^2;
>> simple(a)
simplify:
-13/(3*x-2)^2
radsimp:
-13/(3*x-2)^2
combine(trig):
-13/(9*x^2-12*x+4)
factor:
-13/(3*x-2)^2
expand:
2/(3*x-2)-6/(3*x-2)^2*x-9/(3*x-2)^2
combine:
2/(3*x-2)-(6*x+9)/(3*x-2)^2
convert(exp):
2/(3*x-2)-(6*x+9)/(3*x-2)^2
convert(sincos):
2/(3*x-2)-(6*x+9)/(3*x-2)^2
convert(tan):
2/(3*x-2)-(6*x+9)/(3*x-2)^2
collect(x):
2/(3*x-2)-(6*x+9)/(3*x-2)^2
ans =
-13/(3*x-2)^2

2. ---------------------------------------------------------------------------------------------------------
2)
>> syms x;
>> y=(2*x+3)/(3*x-2);
>> diff(f)
??? Undefined function or variable 'f'.
>> syms x;
>> y=(2*x+3)/(3*x-2);
>> diff(y)
ans =
2/(3*x-2)-3*(2*x+3)/(3*x-2)^2
>> 2/(3*x-2)-3*(2*x+3)/(3*x-2)^2
ans =
2/(3*x-2)-(6*x+9)/(3*x-2)^2
>> a=2/(3*x-2)-(6*x+9)/(3*x-2)^2;
>> simple(a)
simplify:
-13/(3*x-2)^2
radsimp:
-13/(3*x-2)^2
combine(trig):
-13/(9*x^2-12*x+4)
factor:
-13/(3*x-2)^2
expand:
2/(3*x-2)-6/(3*x-2)^2*x-9/(3*x-2)^2

3. combine:
2/(3*x-2)-(6*x+9)/(3*x-2)^2
convert(exp):
2/(3*x-2)-(6*x+9)/(3*x-2)^2
convert(sincos):
2/(3*x-2)-(6*x+9)/(3*x-2)^2
convert(tan):
2/(3*x-2)-(6*x+9)/(3*x-2)^2
collect(x):
2/(3*x-2)-(6*x+9)/(3*x-2)^2
ans =
-13/(3*x-2)^2
>> syms x;
>> y=i/((x+2)^(1/2));
>> diff(y)
ans =
-1/2*i/(x+2)^(3/2)
>> a=-1/2*i/(x+2)^(3/2);
>> simple(a)
simplify:
-1/2*i/(x+2)^(3/2)
radsimp:
-1/2*i/(x+2)^(3/2)

4. combine(trig):
-1/2*i/(x+2)^(3/2)
factor:
-1/2*i/(x+2)^(3/2)
expand:
-1/2*i/(x+2)^(3/2)
combine:
-1/2*i/(x+2)^(3/2)
convert(exp):
-1/2*i/(x+2)^(3/2)
convert(sincos):
-1/2*i/(x+2)^(3/2)
convert(tan):
-1/2*i/(x+2)^(3/2)
collect(x):
-1/2*i/(x+2)^(3/2)
ans =
-1/2*i/(x+2)^(3/2)
>> syms x;
>> y=x*(x+1)^(1/2);
>> diff(y)
ans =

5. (x+1)^(1/2)+1/2*x/(x+1)^(1/2)
>> syms x;
>> y=(4-x^2)^(1/2);
>> diff(y)
ans =
-1/(4-x^2)^(1/2)*x
>> syms x;
>> y
y=
(4-x^2)^(1/2)
>> y
y=
(4-x^2)^(1/2)
>> y=(2*x+3)^(1/3);
>> diff(y)
ans =
2/3/(2*x+3)^(2/3)
>> syms x;
>> y=(x^2-1)/(x^2+1);
>> diff(y)
ans =
2*x/(x^2+1)-2*(x^2-1)/(x^2+1)^2*x
>> syms x;
>> symy a;
??? symy a;
|
Error: Missing operator, comma, or semicolon.
>> syms x;syms a;
>> y=((a*x)^(1/2))+a/((a*x)^(1/2));
>> simple(diff(y))
simplify:

6. 1/2*a*(x-1)/x/(a*x)^(1/2)
radsimp:
1/2*a^(1/2)*(x-1)/x^(3/2)
combine(trig):
1/2*(a^2*x-a^2)/(a*x)^(3/2)
factor:
1/2*a^2*(x-1)/(a*x)^(3/2)
expand:
1/2*a/(a*x)^(1/2)-1/2*a^2/(a*x)^(3/2)
combine:
1/2*a/(a*x)^(1/2)-1/2*a^2/(a*x)^(3/2)
convert(exp):
1/2*a/(a*x)^(1/2)-1/2*a^2/(a*x)^(3/2)
convert(sincos):
1/2*a/(a*x)^(1/2)-1/2*a^2/(a*x)^(3/2)
convert(tan):
1/2*a/(a*x)^(1/2)-1/2*a^2/(a*x)^(3/2)
collect(x):
1/2*a/(a*x)^(1/2)-1/2*a^2/(a*x)^(3/2)
ans =

7. 1/2*a^2*(x-1)/(a*x)^(3/2)