导数(一)

常用求导公式

(1) (C)’=0
(2) (x^u)’=ux^{u-1}
(3) (sin(x))’=cos(x)
(4) (cos(x))’=-sin(x)
(5) (tan(x))’= -sec^2(x)
(6) (csc(x))’=-csc^2(s)
(7) (a^x)’=a^xlnx
(8) (e^x)’=e^x
(9) (linx)’= \dfrac{1}{x}
(10) (loga^x)’=\dfrac{1}{xlina}

(11) (a^x)’=ax^{a-1}

四则法则

(1) (u(x)\pm{ v(x)})’=u’(x)\pm{v(x)’}

(2) (u(x)v(x))’ = u’(x)v(x)+u(x)v’(x)

(3) 设v(x)\not =0 \quad (\dfrac{u(x)}{v(x)})’=\dfrac{u’(x)v(x)-u(x)v’(x)}{v^2(x)}

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