derivative of ace^{-e^{c(b-x}+c(b-x)})

解答

\frac{d}{d x} (a c e^{- e^{c (b - x)} + c (b - x)})

a c e^{- e^{c (b - x)} + c (b - x)} (c e^{c (b - x)} - c)

求解步骤

\frac{d}{d x} (a c e^{- e^{c (b - x)} + c (b - x)})

将常数提出:

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

= a c \frac{d}{d x} (e^{- e^{c (b - x)} + c (b - x)})

使用连锁律:

e^{- e^{c (b - x)} + c (b - x)} \frac{d}{d x} (- e^{c (b - x)} + c (b - x))

= e^{- e^{c (b - x)} + c (b - x)} \frac{d}{d x} (- e^{c (b - x)} + c (b - x))

\frac{d}{d x} (- e^{c (b - x)} + c (b - x)) = c e^{c (b - x)} - c

= a c e^{- e^{c (b - x)} + c (b - x)} (c e^{c (b - x)} - c)

\int tan (x) sec^{6} (x) d x

d er i v a t i v e 7 t + 4 t^{7}

\frac{d}{d x} ((4 x + e^{- z^{2}})^{3})

\int x x - 21 d x

d er i v a t i v e f (x) = \frac{7 x - 4}{- 3 x + 3}