derivative of-ln(2*2^{-x})

解答

\frac{d}{d x} (- ln (2) \cdot 2^{- x})

ln^{2} (2) \cdot 2^{- x}

求解步骤

\frac{d}{d x} (- ln (2) \cdot 2^{- x})

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= - ln (2) \frac{d}{d x} (2^{- x})

使用指数法则:

a^{b} = e^{b l n (a)}

2^{- x} = e^{(- x) l n (2)}

= - ln (2) \frac{d}{d x} (e^{(- x) l n (2)})

使用连锁律:

e^{(- x) l n (2)} \frac{d}{d x} ((- x) ln (2))

= e^{(- x) l n (2)} \frac{d}{d x} ((- x) ln (2))

\frac{d}{d x} ((- x) ln (2)) = - ln (2)

= - ln (2) e^{(- x) l n (2)} (- ln (2))

化简

- ln (2) e^{(- x) l n (2)} (- ln (2)) : ln^{2} (2) \cdot 2^{- x}

= ln^{2} (2) \cdot 2^{- x}

\int_{0}^{3} x x + 1 d x

\frac{d}{d t} (e^{4 (e^{t} - 1)})

\frac{d}{d x} (\frac{( 4 x + a 1 + x )}{x ^{2} - 1})

in v erse l a pl a ce \frac{16}{( s - 1 ) ( s + 1 )}

in v erse l a pl a ce \frac{2}{s ^{2} ( s ^{2} + 25 )}