Deriv Tutorial: Variables

Here, we notice that the function y is exactly equal to the independent variable t. Therefore, the derivative is just one, which we can see by thinking about slopes or by using the power rule:

The derivative of the independent variable of an expression is one.

We can see this by thinking about the slope of a line: if

m x + b

then the slope, y' is just

Thus, if

then the slope, which is the derivative, is just one:

Another way of thinking about this is the power rule: The derivative of any power function is the product of its exponent and a power function with the exponent decreased by one. So if

	y	=	x
		=	x¹,

then

y'	=	1 ( x^1-1 )
	=	1 ( x⁰ )
	=	1 ( 1 ) = 1

Derivatives of Variables