First derivative

diff(3*x^6+5*x^4,x);

diff(-(1/4)*x^6+3*x,x);

diff(2*x^(-6)+5*x^5,x);

diff(4/x^5+2/3,x);

diff(-18/x^5-2*x^5,x);

diff(%e^(x^2+2*x+5),x);

Derivatives of higher order

diff(x^3,x,2);

diff(x^3,x,3);

diff((x^3-2)/2*x^2,x,2);

diff((x^3+5*x-4)/(x^2-2),x,3);

diff((sin(t)+t)/cos(t),t,2);

diff(%e^x/cos(x),x,2);

diff((x^2+5*x+6)/(%e^(2*x)-sin(x)),x,2);

Partial derivatives

diff(x^3*y + y^3*x,x,1);

diff(x^3*y + y^3*x,y,1);

diff(sin(x+y^2),x,1);

diff(sin(x+y^2),y,1);

diff(log(x^2 + y^4 + 1),x,1);

diff(log(x^2 + y^4 + 1),y,1);

diff(x*e^(xy^2),x,1);

diff(x*e^(xy^2),y,1);

Higher order partial derivatives

diff(x*e^(xy^2),x,1,y,1);

diff(log(x + y^3 + z^5),x,1,y,1,z,1);

The total differential

diff(x^2*y+y^2*x);

%, del(x) = dx, del(y ) = dy ;

The gradient

jacobian([x^2-2*x*y+6*x-2*y+1],[x,y]);

jacobian([%e^(x*y)],[x,y]);

Jacobian matrix

f(x,y):= [x^2-2*x*y+6*x-2*y+1,x^3*y+y^2*x^3];

jacobian(f(x,y),[x,y]);

g(x,y):=[%e^(x*y),sin(x*y)];

jacobian(g(x,y),[x,y]);