# How do you graph the derivative of f(x) = x^2?

Feb 13, 2016

Plot y = 2x, so it will be a straight line, passing through the origin with a gradient of 2.

#### Explanation:

Plot y = 2x, so it will be a straight line, passing through the origin with a gradient of 2.

The derivative of f(x) is:
f'(x) = 2x

Feb 13, 2016

$f ' \left(x\right) = 2 x$ and is hence a linear graph so a straight line of slope $2$ and intercept $\left(0 , 0\right)$.

#### Explanation:

The derivative of any function at any point represents the gradient of the tangent of that function at the point.

The derivative of this particular quadratic function is $\frac{d}{\mathrm{dx}} {x}^{2} = 2 x$.

This represents a linear function and hence a straight line graph of gradient 2 and intercept the origin.
It is hence drawn as follows :

graph{2x [-11.25, 11.25, -5.625, 5.625]}