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Rules for differentiation of general functions

{d \over dx} cf(x) = c{d \over dx} f(x)

{d \over dx} (f(x) + g(x)) = f'(x) + g'(x)

{d \over dx} (f(x) - g(x)) = f'(x) - g'(x)

{d \over dx} (f(x)g(x)) = f'(x)g(x) + f(x)g'(x)

{d \over dx} \left({f(x) \over g(x)}\right) = {f'(x)g(x) - f(x)g'(x) \over (g(x))^2}

{d \over dx} f(x)^{g(x)} = f(x)^{g(x)}\left(f'(x){g(x) \over f(x)} + g'(x)\ln f(x)\right),\qquad f(x) > 0

{d \over dx} f(g(x)) = f'(g(x))g'(x)
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