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A: TABLE OF BASIC DERIVATIVES Let u = u(x) be a differentiable function of the independent variable x, that is u(x) exists. (A) The Power Rule : Examples : d dx {un} = nu n−1. u ddx {(x3 + 4x + 1)3/4} = 34 (x3 + 4x + 1)−1/4.(3x2 + 4)d dx {u} = 12 u.u d dx { 2 − 4x2 + 7x5} = 1 2 2 − 4x2 + 7x5 (−8x + 35x4) d dx {c} = 0 , c is a constant ddx {6} = 0 , since ≅ 3.14 is a constant.

Differentiation Formulas List. 1. Basic Differentiation Formulas. Page 2. 2. Differentiation Formulas For Trigonometric Functions. Page 3 ...

Table of derivatives Introduction This leaflet provides a table of common functions and their derivatives. 1. The table of derivatives y = f(x) dy dx = f′(x) k, any constant 0 x 1 x2 2x x3 3x2 xn, any constant n nxn−1 ex ex ekx kekx lnx = log e x 1 x sinx cosx sinkx kcoskx cosx −sinx coskx −ksinkx tanx = sinx cosx sec2 x tankx ksec2 kx ...

Integrate the partial fraction decomposition (P.F.D.). For each factor in the denominator we get term(s) in the decomposition according to the following table.

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

(Inverse function) If y = f(x) has a non-zero derivative at x and the inverse function x = f. -1. (y) is continuous at corresponding point y, then x = f.

Extending the table of derivatives mc-TY-table2-2009-1 In this unit we continue to build up The Table of Derivatives using rules described in other units. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so …

Differentiation Formulas d dx k = 0. (1) d dx. [f(x) ± g(x)] = f (x) ± g (x). (2) d dx. [k · f(x)] = k · f (x). (3) d dx. [f(x)g(x)] = f(x)g (x) + g(x)f (x) ...

TABLE OF DERIVATIVES. FUNCTION DERIVATIVE. C. 0 cx c xa axa−1 sinx cosx cosx. −sinx ... RULES FOR DERIVATIVES. Rule for addition: If h(x) = f(x) + g(x).

DIFFERENTIATION TABLE (DERIVATIVES) Notation: u = u(x) and v = v(x) are differentiable functions of x; c, n, and a > 0 are constants; u0 = du dx is the derivative of u with respect to (w.r. to) x (1) x0 = 1 (2) c0 = 0 (3) (cu)0 = c·u0 (4) (u±v) 0= u0 ±v (5) (uv) 0= u v +v0u (6) u v 0 = u0v −v0u v2 (7) (un) 0= nun−1u (a) 1 u 0 = − u0 ...

Derivative Table 1. dx dv dx du (u v) dx d ± = ± 2. dx du (cu) c dx d = 3. dx du v dx dv (uv) u dx d = + 4. dx dv wu dx du vw dx dw (uvw) uv dx d = + + 5. v2 dx dv u dx du v v u dx d − = 6. (Chain rule) If y = f(u) is differentiable on u = g(x) and u = g(x) is differentiable on point x, then the composite function y = f(g(x)) is ...

or . 4. Definition of a derivative. 5. To find the maximum and minimum values of a function y = f(x), locate.

Table of Derivatives. Throughout this table, a and b are constants, independent of x. ... Table of Indefinite Integrals. Throughout this table, a and b are ...

A: TABLE OF BASIC DERIVATIVES. Let u = u(x) be a differentiable function of the independent variable x , that is u (x) exists. (A) The Power Rule :.

This leaflet provides a table of common functions and their derivatives. 1. The table of derivatives y = f(x) dy dx.