Confused how to differentiate f(x) = 2/3 (x^3) + 2(x^2) + x - 1/2

[wduk]

I have the following function

f(x) = 2/3 (x^3) + 2(x^2) + x - 1/2

So i got:

f1(x) = 2x^2 + 4x + 1 - 1/2

But my book has this :

f1 (x) = 2x^2 + 4x + 1

I'm a bit confused how - 1/2 gets ignored here, trying to work out how to understand what calculation occurs on the -1/2 to result in 0?

 

[Deleted member 4993]

I have the following function

f(x) = 2/3 (x^3) + 2(x^2) + x - 1/2

So i got:

f1(x) = 2x^2 + 4x + 1 - 1/2

But my book has this :

f1 (x) = 2x^2 + 4x + 1

I'm a bit confused how - 1/2 gets ignored here, trying to work out how to understand what calculation occurs on the -1/2 to result in 0?

Rate of change of "a constant" is equal to zero - that is one of the properties of "constant". In this problem (-1/2) is a constant.

 

[Otis]

... trying to work out how to understand what calculation occurs on the -1/2 to result in 0?

In calculus, x^0 = 1 for all x.

So you may think of the constant term in your function as -1/2*x^0, and then apply the Power Rule:

0*(-1/2)*x^(0-1)

See that multiplication by zero in front?

If you were to replace -1/2 with any other constant, the derivative calculation would end up the same: zero.

As Subhotosh alluded to, the derivative is the RATE at which a quantity changes. But, if that quantity is a constant, then it is not changing at all; hence, its rate of change must be zero.

Now that you understand, you no longer need to do the calculation with the Power Rule above. Just remember: the derivative of a constant is zero.