Transcription of DIFFERENTIATION TABLE (DERIVATIVES)
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DIFFERENTIATION TABLE (DERIVATIVES)
DIFFERENTIATION TABLE (DERIVATIVES)Notation:u=u(x) andv=v(x) are differentiable functions ofx;c,n, anda>0 are constants;u =dudxis the derivative ofuwithrespect to ( to)x(1)x = 1(2)c = 0(3) (cu) =c u (4) (u v) =u v (5) (uv) =u v+v u(6)(uv) =u v v uv2(7) (un) =nun 1u (a)(1u) = u u2(b) ( u) =u 2 u(8) (sinu) = cosuu (9) (cosu) = sinuu (10) (tanu) = sec2uu (11) (cotu) = csc2uu (12) (secu) = secutanuu (13) (cscu) = cscucotuu (14) (au) =au(lna)u (15) (eu) =euu (16) (lnu) =u u(17) (sin 1u) =u 1 u2(18) (cos 1u) = u 1 u2(19) (tan 1u) =u 1 +u2(Note: sin 1= arcsin, cos 1= arccos, tan 1= arctan. )12 INTEGRATION TABLE (INTEGRALS)Notation:f(x) andg(x) are any continuous functions;u=u(x) isdifferentiable function ofx;du=dudxdx=u dx;c,n, anda>0 areconstants(1) (f(x) +g(x))dx= f(x)dx+ g(x)dx(2) cf(x)dx=c f(x)dx(3) undu=un+1n+ 1+C,n6= 1(a) 1udu= duu= ln|u|+C(b) 1 udu= du u= 2 u+C(c) du=u+C(4) eudu=eu+C(5) sinudu= cosu+C(6) cosudu= sinu+C(7) sec2udu= 1cos2udu= tanu+C(8) csc2udu= 1sin2udu= cotu+C(9) 1u2+a2du= duu2+a2=1aarctanua+C(10) 1 a2 u2du= du a2 u2=1aarcsinua+C
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
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