This page titled Appendix A: Table of Derivatives is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Gilbert Strang & Edwin “Jed” Herman via source content that was edited to the style and standards of the LibreTexts platform.

RULES FOR DERIVATIVES Rule for addition: If h(x) = f(x)+g(x) OR d dx (u+v) = du dx + dv dx Then h0(x) = f0(x)+g0(x) Rule for scalar multiplication: If h(x) = af(x) OR d dx (au) = a du dx Then h0(x) = af0(x) Product rule: If h(x) = f(x)g(x) OR d dx (uv) = du dx v +u dv dx Then h0(x) = f0(x)g(x)+f(x)g0(x) Quotient rule: If h(x) = f(x) g(x) OR d ...

If the derivatives g0(x) and f 0(g(x)) both exist, and F(x) = f(g(x)), then F (x) exist and F 0(x) = f0(g(x))g (x):

Feb 21, 2022 · Derivatives for Elementary Trancendental Functions \( \displaystyle \frac {d} {dx} \textcolor{orange}{x}^\textcolor{magenta}{n} = \textcolor{magenta}{n}\textcolor{orange}{x}^{\textcolor{magenta}{n}-1} \)

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Table of Derivatives. Derivative Identities. Min, Max, Critical Points, Asymptotes, Concavity, Inflection, etc.

A list of commonly needed differentiation formulas, including derivatives of trigonometric, inverse trig, logarithmic, exponential and hyperbolic types.

This leaflet provides a table of common functions and their derivatives. 1. The table of derivatives. dy 1. In each case, use the table of derivatives to write down. w) y = ex/2 dy 2. You should be able to use the table when other variables are used. …

Table 2.1, choose Yp in the same line and determine its undetermined coefficients by substituting Yp and its derivatives into (4). (b) Modification Rule. If a term in your choice for Yp happens to be a solution of the homogeneous ODE corresponding to (4), multiply this term by x (or by x 2 if this solution corresponds to a double root of the

Table of Derivatives In the formulas given below, it's assumed that C , k and n are real numbers, m is a natural number, f, g, u, v are functions of the real variable x , and the base a of the exponential and logarithmic functions satisfies the conditions a > 0 , a ≠ 1 .