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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.

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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