B Derivative rules

For the calculation of the derivative, specific rules depending on the original function have to be applied:

Function Derivative Rule
\(f(x) = x^n\) \(f'(x) = n \cdot x^{n-1}\) Power rule
\(f(x) = g(x) \pm h(x)\) \(f'(x) = g'(x) \pm h'(x)\) Sum and difference rule
\(f(x) = g(x) \cdot h(x)\) \(f'(x) = g'(x) \cdot h(x) + g(x) \cdot h'(x)\) Product rule
\(f(x) = \frac{g(x)}{h(x)}\) \(f'(x) = \frac{g'(x) \cdot h(x) - g(x) \cdot h'(x)}{\big(h(x)\big)^2}\) Quotient rule
\(f(x) = h\big(g(x)\big)\) \(f'(x) = h'\big(g(x)\big) \cdot g'(x)\) Chain rule