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Created by sabasta
about 9 years ago
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Copied by Mathe Queen
about 8 years ago
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Question | Answer |
f(x)=ax |
f′(x)=ax⋅lna |
f(x)=sinx |
f′(x)=cosx |
f(x)=cosx |
f′(x)=−sinx |
f(x)=C⋅g(x) |
f′(x)=C⋅g′(x) |
f(x)=[g(x)]n |
f′(x)=n⋅[g(x)]n−1⋅g′(x) |
f(x)=ex |
f′(x)=ex |
f(x)=eg(x) |
f′(x)=eg(x)⋅g′(x) |
f(x)=sing(x) |
f′(x)=cosg(x)⋅g′(x) |
f(x)=cosg(x) |
f′(x)=−sing(x)⋅g′(x) |
f(x)=tanx |
f′(x)=1cos2⋅x |
f(x)=lnx |
f′(x)=1x |
f(x)=lng(x) |
f′(x)=g′(x)g(x) |
f(x)=logag(x) |
f′(x)=g′(x)g(x)⋅lna |
f(x)=logax |
f′(x)=1x⋅lna |
f(x)=ag(x) |
f′(x)=ag(x)⋅lna⋅g′(x) |
Kettenregel
f(x)=f(g(x)) |
f′(x)=f′(g)⋅g′(x) |
Produktregel
f(x)=u(x)⋅v(x) |
f′(x)=u′(x)⋅v(x)+u(x)⋅v′(x) |
Summenregel
f(x)=u(x)±v(x) |
f′(x)=u′(x)±v′(x) |
Quotientenregel
f(x)=u(x)v(x) |
f′(x)=u′(x)⋅v(x)−u(x)⋅v′(x)[v(x)]2 |
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