Second Derivatives

MathsDirect

If you differentiate y w.r.t. x, you get

which tells you the rate at which y is changing with x.

You can continue differentiating, to find how the gradient varies with x. This second derivative is written,

and reads as "d two y, by dx squared."

You can continue to the third derivative,

and so on. These are used in further maths, but for single maths, you are only required to use the second and third derivatives.

Below are a few examples of finding the second derivative.

Differentiate the following functions twice.