This is a summary of differentiation rules, that is, rules for computing the derivative of a function in calculus. Combining this rule with the linearity of the derivative and the addition rule permits the computation of the derivative of any all integration differentiation formulas pdf. The reciprocal rule can be derived from the quotient rule.
This can be derived from product rule. The elementary power rule generalizes considerably.
1 when a is any non-zero real number and x is positive. 0 yields a complex number. This formula is the general form of the Leibniz integral rule and can be derived using the fundamental theorem of calculus.
Some rules exist for computing the nth derivative of functions, where n is a positive integer. Mendelson, Schuam’s Outline Series, 2009, ISBN 978-0-07-150861-2.
Spiegel, Schuam’s Outline Series, 2010, ISBN 978-0-07-162366-7. These rules are given in many books, both on elementary and advanced calculus, in pure and applied mathematics. Liu, Schuam’s Outline Series, 2009, ISBN 978-0-07-154855-7.
The Cambridge Handbook of Physics Formulas, G. Woan, Cambridge University Press, 2010, ISBN 978-0-521-57507-2.