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General differentiation rules

Linearity

Product rule

Reciprocal rule

Quotient rule

Chain rule

where (f g)(x) is defined as f(g(x))

Derivative of inverse function

for any differentiable function f of a real argument and with real values, when the indicated

compositions and inverses exist.

Generalized power rule

Derivative of implicit function

If implicit function y(x) is defined as F(x,y(x)) = 0

then

Derivative of parametrically defined function

If a function y(x) defined parametrically

then