Differentiation Examples 

by 

Christopher P. Benton, Ph.D. 

 

Here are some basic first derivatives using MAPLE. 

 

diff(x^2, x); 1 

2*x 

diff(sqrt(x), x); 1 

1/2/x^(1/2) 

diff(y^10, y); 1 

10*y^9 

diff(x*sqrt(1+x), x); 1 

(1+x)^(1/2)+1/2*x/(1+x)^(1/2) 

 

We can also use tools from the expression pallete to enter derivatives. 

 

diff(x^2, x) 

2*x 

diff(sqrt(x), x) 

1/2/x^(1/2) 

diff(y^10, y) 

10*y^9 

diff(x*sqrt(x+1), x) 

(1+x)^(1/2)+1/2*x/(1+x)^(1/2) 

Here's are a couple of ways to do higher order derivatives. 

 

diff(x^5, x, x); 1 

20*x^3 

diff(x^5, `$`(x, 2)); 1 

20*x^3 

We can also differentiate vectors. 

 

r := [t, t^2, t^3]; 1 

[t, t^2, t^3] 

diff(r, t) 

[1, 2*t, 3*t^2] 

And finally, we can do lots of partial derivatives. 

 

diff(x^5*y^3, x); 1 

5*x^4*y^3 

diff(x^5*y^3, y); 1 

3*x^5*y^2 

diff(x^5*y^3, x, y); 1 

15*x^4*y^2 

diff(x^5*y^3, y, x); 1 

15*x^4*y^2