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Diff_Int_table

# Diff_Int_table - Some basic derivatives f(x xn ln(x cos(x...

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Some basic derivatives: f ( x ) f ( x ) f ( x ) f ( x ) x n nx n - 1 e x e x ln( x ) 1 /x sin( x ) cos( x ) cos( x ) - sin( x ) tan( x ) sec 2 ( x ) cot( x ) - cosec 2 ( x ) sec( x ) sec( x ) tan( x ) cosec( x ) - cosec( x ) cot( x ) tan - 1 ( x ) 1 / (1 + x 2 ) sin - 1 ( x ) 1 / 1 - x 2 for | x | < 1 cos - 1 ( x ) - 1 / 1 - x 2 for | x | < 1 sinh( x ) cosh( x ) cosh( x ) sinh( x ) tanh( x ) sech 2 ( x ) coth( x ) - cosech 2 ( x ) sech( x ) - sech( x ) tanh( x ) cosech( x ) - cosech( x ) coth( x ) sinh - 1 ( x ) 1 / x 2 + 1 cosh - 1 ( x ) 1 / x 2 - 1 for x > 1 tanh - 1 ( x ) 1 / (1 - x 2 ) for | x | < 1 coth - 1 ( x ) - 1 / ( x 2 - 1) for | x | > 1 Basic rules for differentiation and integration: d d x ( f ( x ) + g ( x ) ) = d d x f ( x ) + d d x g ( x ) = f ( x ) + g ( x ) derivative of a sum d d x ( cf ( x ) ) = c d d x f ( x ) = cf ( x ) derivative with a constant factor d d x ( f ( x ) g ( x ) ) = f ( x ) g ( x ) + f ( x ) g ( x ) derivative of a product “first times derivative of second plus second times derivative of first” d d x f ( x ) g ( x ) = g ( x ) f ( x ) - f ( x ) g ( x ) g 2 ( x ) derivative of a quotient “bottom times derivative of top minus top times derivative of bottom, over bottom squared” d d x f ( g ( x ) ) = f ( g ( x ) ) g ( x ) chain rule, or function of a function rule

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Diff_Int_table - Some basic derivatives f(x xn ln(x cos(x...

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