FONCTION | DÉRIVÉE |
a.u | a.du |
u + v + w | du + dv + dw |
u.v | (v.du + u.dv) / v2 |
un | n.un-1.du |
uv | v.uv-1.du + uv.ln(u).dv |
eu | eu.du |
ea.u | a.ea.u.du |
au | au.ln(a).du |
ln(u) | u-1.du |
loga(u) | u-1.loga(e).du |
uu | uu.[1+ln(u)].du |
sin(u) | cos(u).du |
cos(u) | -sin(u).du |
tan(u) | 1 / cos2(u) . du |
cotan(u) | - 1 / sin2(u) . du |
1 / cos(u) | tan(u) / cos(u) . du |
1 / sin(u) | - cotan(u) / sin(u) . du |
sin-1(u) | (1-u2)-½.du |
cos-1(u) | -(1-u2)-½.du |
tan-1(u) | (1+u2)-1.du |
cotan-1(u) | -(1+u2)-1.du |
1 / cos-1(u) | u-1.(u2-1)-½.du |
1 / sin-1(u) | -u-1.(u2-1)-½.du |
sinh(u) | cosh(u).du |
cosh(u) | sinh(u).du |
tanh(u) | 1 / cosh2(u) . du |
cotanh(u) | - 1 / sinh2(u) . du |
1 / cosh(u) | - tanh(u) / cosh(u) . du |
1 / sinh(u) | - cotanh(u) / sinh(u) . du |
sinh-1(u) | (u2+1)-½.du |
cosh-1(u) | (u2-1)-½.du |
tanh-1(u) | (1-u2)-1.du |
cotanh-1(u) | -(u2-1)-1.du |
1 / cosh-1(u) | u-1.(1-u2)-½.du |
1 / sinh-1(u) | -u-1.(u2+1)-½.du |