1)

(%i1) diff((log(1+x^4+y^4)/sqrt(x^2+y^2)),x,2);

Result

(%i2) diff((log(1+x^4+y^4)/sqrt(x^2+y^2)),y,2);

Result

(%i3) diff((log(1+x^4+y^4)/sqrt(x^2+y^2)),x,1,y,1);

Result

(%i4) diff((log(1+x^4+y^4)/sqrt(x^2+y^2)),y,1,x,1);

Result

2)

(%i5) define(y(x),sqrt(x)+sqrt(y)=1);

Result

(%i11) diff(y(x), x);

Result

(%i13) diff(y(x), x,2);

Result

3)

(%i20) A:integrate(sqrt(%e^x-1),x);

Result

(%i22) rat(diff(A,x));

Result

(%i18) expand(%);

Result

4)

(%i23) 'integrate(1/sqrt(1-x^2),x,0,1)$ %=ev(%, nouns);

Result

5)

(%i25) sum(1/k^4, k, 1, inf), simpsum;

Result

6)

(%i28) limit(log(x)/%e^x,x,inf);

Result

7)

(%i29) t:taylor(sin(x),x,0,5);

Result

(%i31) define(f(x),t);

Result

(%i32) wxplot2d([f(x),sin(x)], [x,-%pi,%pi])$

Result


Created with wxMaxima.