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

Mar 6, 2018

The derivative is $4 x$.

#### Explanation:

For this, we can use the power rule: $\setminus \frac{d}{\mathrm{dx}} a {x}^{n} = n a {x}^{n - 1}$.

So, if we have $y = 2 {x}^{2} - 5$, the only term that involves an x is the $2 {x}^{2}$, 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, $\setminus \frac{d}{\mathrm{dx}} 2 {x}^{2} = 2 \left(2\right) {x}^{2 - 1} = 4 x$.

Mar 6, 2018

4x

#### Explanation:

the power rule goes as

$\frac{d}{\mathrm{dx}} c \cdot {x}^{n} = n \cdot c \cdot {x}^{n - 1}$

$2 {x}^{2} - 5$

$= 2 {x}^{2} - 5 {x}^{0}$

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

=
$2 \cdot 2 {x}^{2 - 1} - 0 \cdot 5 \cdot {x}^{0 - 1}$

=
$4 x$
=

and that's it