Transcription of A: TABLE OF BASIC DERIVATIVES
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A: TABLE OF BASIC DERIVATIVES
A: TABLE OF BASIC DERIVATIVESLetu=u(x)be a differentiable function of the independent variablex, that isu (x)exists.(A) The Power Rule :Examples :ddx{un} =nun ddx{(x3+4x+1)3/4} =34(x3+4x+1) 1/4.(3x2+4)ddx{u} = ddx{2 4x2+7x5} =12 2 4x2+7x5( 8x+35x4)ddx{c} =0 ,cis a constantddx{ 6} =0 , since is a constant.(B) The Six Trigonometric Rules :Examples :ddx{sin(u)} =cos(u).u ddx{sin(x3)} =cos(x3). 3x2ddx{cos(u)} = sin(u).u ddx{cosx)} = sin(x).12xddx{tan(u)} =sec2(u).u ddx{tan{5x2)} =sec2(5x 2).( 10x 3)ddx{cot(u)} = csc2(u).u ddx[cot{sin(2x)}] = csc2{sin(2x)}. 2cos(2x).ddx{sec(u)} =sec(u)tan(u).u ddx{sec(4x)} =sec(4x)tan(4x).14x 3/4ddx{csc(u)} = csc(u)cot(u).u ddx{csc(8x 7)} = csc(8x 7)cot(8x 7). 8(C) The Six Hyperbolic Rules :Examples :ddx{sinh(u)} =cosh(u).u ddx{sinh(3x)} =cosh(3x).13x 2/3ddx{cosh(u)} =sinh(u).u ddx{cosh(sec(x)} =sinh{sec(x)}. sec(x)tan(x)ddx{tanh(u)} =sech2(u).u ddx[tanh{x3+sin(x2)}] =sech2{x3+sin(x2)}.}
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.
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