| Rule | Function | Derivative | Basic |
| Constant Function Rule | \(f(x) = k\) | \(f'(x) = 0\) | |
| Linear Function Rule | \(f(x) = x\) | \(f'(x) = 1\) | |
| Sum / Difference | \(h = f \pm g \) | \(h' = f' \pm g' \) | \([c + f(x)]' = f(x)' \) |
| Product Rule | \(h = fg \) | \(h' = f'g + fg' \) | \([kg(x)]' = kg'(x)\) |
| Extended Product Rule | \(p = fgh \) | \(p' = f'gh + fg'h + fgh' \) | |
| Power Rule | \(f = g^n \) | \(f = ng^{~n-1}g' \) | \(x^n \Rightarrow nx^{n-1}\) |
| Quotient Rule | \(h = {f \over g}\) | \(h' = {f'g-fg' \over g^2}\)\(,~g \ne 0\) | |
| Chain Rule | \(h(x) = f(g(x))\) | \(h'(x) = f'(g(x)) \times g'(x)\) | |
| Exponent Function | \(f(x) = b^{~g(x)}\) | \(f'(x) = b^{~g(x)} \ln b \times g'(x)\) | \(b^{~x} \Rightarrow b^{~x} \ln b\) |
| \(e\) | \(f(x) = e^x\) | \(f'(x) = e^x\) \(e = \lim \limits_{n \to \infty } {(1+ {1 \over n})^n}~,~\ln x = \log_{e}x \) |
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| Logarithm | \(f(x) = \log_{b} g(x)\) | \( f'(x) = {g'(x) \over g(x) \ln b} \) (chain rule) |
\( \log_{b} x \Rightarrow {1 \over x \ln b}\) |
| Natural Logarithm | \(f(x) = \ln g(x)\) | \(f'(x) = {g'(x) \over g(x)} \) | \(\ln x \Rightarrow {1 \over x}\) |
| Sine Function | \(f(x) = \sin g(x) \) | \(f'(x) = \cos g(x) \times g'(x) \) | \( \sin x \Rightarrow \cos x \) |
| Cosine Function | \(f(x) = \cos g(x) \) | \(f'(x) = \text{-} \sin g(x) \times g'(x) \) | \( \cos x \Rightarrow \text{-} \sin x \) |
| Tangent Function | \(f(x) = \tan g(x) \) | \(f'(x) = \sec^2 g(x) \times g'(x) \) | \( \tan x \Rightarrow \sec^2 x \) |
| Cosecant Function | \(f(x) = \csc x \) | \(f'(x) = \text{-} \csc x \cot x \) use radians |
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| Secant Function | \(f(x) = \sec x \) | \(f'(x) = \sec x \tan x \) use radians |
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| Cotangent Function | \(f(x) = \cot x \) | \(f'(x) = \text{-} \csc^2 x \) use radians |
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| arcSine Function | \(f(x) = \arcsin x \) | \(f'(x) = \frac{1}{\sqrt{1-x^2}} \) | |
| arcCosine Function | \(f(x) = \arccos x \) | \(f'(x) = \text{-} \frac{1}{\sqrt{1-x^2}} \) | |
| arcTangent Function | \(f(x) = \arctan x \) | \(f'(x) = \frac{1}{x^2+1} \) |
\(m_{\text{tangent}} = \text{IROC} = \lim \limits_{h \to 0} {f(a+h)-f(a) \over h} = f'(a) \)
\(m_{\text{secant}} = \text{AROC} = {f(x_{2})-f(x_{1}) \over x_{2} - x_{1} }\)