# How do you calculate (d^2y)/(dx^2) of y=-4x^2+7x?

Nov 2, 2016

$\frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = - 8$

#### Explanation:

You differentiate twice to get the second derivative

So, $y = - 4 {x}^{2} + 7 x$

We differentiate wrt $x$ to get the "First Derivative":
$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(- 4\right) \left(2\right) {x}^{1} + 7$
$\therefore \frac{\mathrm{dy}}{\mathrm{dx}} = - 8 x + 7$

And we differentiate the First Derivative wrt $x$ to get the "Second Derivative":
$\mathrm{dx} = - 8 x + 7$
$\therefore \frac{{d}^{2} y}{{\mathrm{dx}}^{2}} = - 8$