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

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

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

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

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Popular >

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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

\frac{d ^{4}}{d x ^{4}} (e^{\frac{1}{x}})

y = ln (sin (x))

\frac{d}{d x} (x^{2} 7 x - 5)

\frac{d}{d x} (∣ x - 9 ∣)

y^{^{''}} - 2 y^{^{'}} + 37 y = 0

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