### Higher derivatives

So far in this module, we have looked at first and second derivatives. But there's no need to stop differentiating after doing it twice!

Given a function $$f(x)$$, if it can be differentiated $$k$$ times, then we write the $$k$$th derivative as $$f^{(k)}(x)$$. In Leibniz notation, the $$k$$th derivative of $$y$$ with respect to $$x$$ is denoted by $$\dfrac{d^k y}{dx^k}$$.

Higher derivatives are useful for finding polynomial approximations to functions, as we see in the next section.

##### Exercise 24

Let $$n$$ be a positive integer. What is the $$n$$th derivative of the function $$f(x) = x^n$$?

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