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

2 Answers
Mar 6, 2018

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 .

Mar 6, 2018

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