What is the derivative of (e^{-x}-e^5(e^x+e^{-3})) ?

The derivative of (e^{-x}-e^5(e^x+e^{-3})) is -e^{-x-3}-e^{x+5}

What is the first derivative of (e^{-x}-e^5(e^x+e^{-3})) ?

The first derivative of (e^{-x}-e^5(e^x+e^{-3})) is -e^{-x-3}-e^{x+5}

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\frac{d}{d x} ((e^{- x} - e^{5}) (e^{x} + e^{- 3}))

- e^{- x - 3} - e^{x + 5}

Solution steps

\frac{d}{d x} ((e^{- x} - e^{5}) (e^{x} + e^{- 3}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{- x} - e^{5}, g = e^{x} + e^{- 3}

= \frac{d}{d x} (e^{- x} - e^{5}) (e^{x} + e^{- 3}) + \frac{d}{d x} (e^{x} + e^{- 3}) (e^{- x} - e^{5})

\frac{d}{d x} (e^{- x} - e^{5}) = - e^{- x}

\frac{d}{d x} (e^{x} + e^{- 3}) = e^{x}

= (- e^{- x}) (e^{x} + e^{- 3}) + e^{x} (e^{- x} - e^{5})

Simplify

(- e^{- x}) (e^{x} + e^{- 3}) + e^{x} (e^{- x} - e^{5}) : - e^{- x - 3} - e^{x + 5}

= - e^{- x - 3} - e^{x + 5}

What is the derivative of (e^{-x}-e^5(e^x+e^{-3})) ?
The derivative of (e^{-x}-e^5(e^x+e^{-3})) is -e^{-x-3}-e^{x+5}
What is the first derivative of (e^{-x}-e^5(e^x+e^{-3})) ?
The first derivative of (e^{-x}-e^5(e^x+e^{-3})) is -e^{-x-3}-e^{x+5}