The following should provide you enough examples for taking derivatives. In the examples below (y) is the function

and y1 is the derivative.

eaxple one: y= x^2

dy/dx=y1= 2x^1

The symbol ^ means raised to the power.

y=5x^4

dy/dx=y1= 4*5*x^3= 20x^3

y= x^0.5

dy/dx= (0.5)*x^(0.5-1)= 0.5*x^-0.5

Now let us use maple software to do more complicated derivatives.

> y:=5*x^(1/3);

> y1:=diff(y,x);

In the above, y1 is the derivative, (1/3) is the exponent of x, and the derivative is :(1/3)*5 *x^(1/3-1). After simplifying the above expression, we get the derivative shown as :(5/3)divided by (x^2/3). Another example:

>

> y:=6*x^(1/2);

> y1:=diff(y,x);

> y:=1/x;

> y1:=diff(y,x);

> y:=5/x^2;

> y1:=diff(y,x);

> y:= (x+5)^2;

> y1:=diff(y,x);

> y:=(x+5)^3;

> y1:=diff(y,x);

> y:=(x+1)^(1/2);

> y1:=diff(y,x);

> y:=1/(x+1)^(1/2);

> y1:=diff(y,x);

> y:=(x-1)^0.5/(x+1)^0.5;

> y1:=diff(y,x);

> simplify(y1);

Please note that if you want to use maple you must use the expressions exactly as they appear. When you define the function

you specify: y:= x; pay attention to the symbol : * means multiply. ^ means raised.

d iff: means derivative, diff(y,x) means deriavtive with respect to x and so on. More examples to follow

> y:=(x+1)*(x^2-6);

> y1:=diff(y,x);

> y:=(x^3 +6*x-3)*(x^2-1);

> y1:=diff(y,x);

> simplify(y1);

>