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 polynomial. The reciprocal differentiation rules and formulas pdf 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.
Mathematical methods for physics and engineering, K. NIST Handbook of Mathematical Functions, F. Clark, Cambridge University Press, 2010, ISBN 978-0-521-19225-5. This page was last edited on 23 October 2017, at 11:49.
The slope of the tangent line is equal to the derivative of the function at the marked point. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object’s velocity: this measures how quickly the position of the object changes when time advances. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.
The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the “instantaneous rate of change”, the ratio of the instantaneous change in the dependent variable to that of the independent variable. Derivatives may be generalized to functions of several real variables.