Question

What is the derivative of `y = 2x^2 - 5`?

Answer 1

The derivative is `4x`.

Explanation:

For this, we can use the power rule: `\frac d dx ax^n = nax^(n-1)`.

So, if we have `y=2x^2 -5`, the only term that involves an x is the `2x^2`, so that is the only term we have to find the derivative of. (The derivative of a constant such as `-5` will always be 0, so we don't have to worry about it since adding or subtracting 0 won't change our overall derivative.)

Following the power rule, `\frac d dx 2x^2 = 2(2)x^(2-1) = 4x`.

Answer 2

4x

Explanation:

the power rule goes as

`d/dx c*x^n = n*c*x^(n-1)`

`2x^2 - 5`

`= 2x^2 - 5x^0`

the 2 and 0 comes down to the front and you subtract one from the power

=
`2*2x^(2-1) - 0*5*x^(0-1)`

=
`4x`
=

and that's it