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# Differentiation Rules

These are the rules that explain how to take derivatives of any functions: from polynomials to trigonometric functions to logarithms.

# Differentiation - Power Rule

What is the derivative of $$\displaystyle y=5 x^{3}+\frac{1}{x^{6}}$$?

What is the derivative of $$-17 x^{16}$$?

If $$f(x) = \displaystyle{\sum_{k=1}^{n} x^k},$$ what is $$\displaystyle{ \lim_{n \rightarrow \infty} \frac{f'(1)}{3n^2+4n+5} }?$$

What is the derivative of $$y = \frac{4}{x}+\frac{4}{x^2}?$$

What is the derivative of $$x^{15}$$?

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