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