What is the derivative of ace^{-e^{c(b-x}+c(b-x)}) ?

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

What is the first derivative of ace^{-e^{c(b-x}+c(b-x)}) ?

The first derivative of ace^{-e^{c(b-x}+c(b-x)}) is ace^{-e^{c(b-x)}+c(b-x)}(ce^{c(b-x)}-c)

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\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)

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

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

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

\frac{d}{d x} (e^{\frac{x ^{2}}{2}})

\int x x - 21 d x

What is the derivative of ace^{-e^{c(b-x}+c(b-x)}) ?
The derivative of ace^{-e^{c(b-x}+c(b-x)}) is ace^{-e^{c(b-x)}+c(b-x)}(ce^{c(b-x)}-c)
What is the first derivative of ace^{-e^{c(b-x}+c(b-x)}) ?
The first derivative of ace^{-e^{c(b-x}+c(b-x)}) is ace^{-e^{c(b-x)}+c(b-x)}(ce^{c(b-x)}-c)