# 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