What is the derivative of (e^{-x}-e^5(e^x+e^{-2})) ?

The derivative of (e^{-x}-e^5(e^x+e^{-2})) is -e^{-x-2}-e^{x+5}

What is the first derivative of (e^{-x}-e^5(e^x+e^{-2})) ?

The first derivative of (e^{-x}-e^5(e^x+e^{-2})) is -e^{-x-2}-e^{x+5}

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Popular >

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

- e^{- x - 2} - e^{x + 5}

Solution steps

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

Apply the Product Rule:

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

f = e^{- x} - e^{5}, g = e^{x} + e^{- 2}

= \frac{d}{d x} (e^{- x} - e^{5}) (e^{x} + e^{- 2}) + \frac{d}{d x} (e^{x} + e^{- 2}) (e^{- x} - e^{5})

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

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

= (- e^{- x}) (e^{x} + e^{- 2}) + e^{x} (e^{- x} - e^{5})

Simplify

(- e^{- x}) (e^{x} + e^{- 2}) + e^{x} (e^{- x} - e^{5}) : - e^{- x - 2} - e^{x + 5}

= - e^{- x - 2} - e^{x + 5}

f (x) = \frac{5 x}{( 1 + x ^{2} )}

\frac{2 x}{( x + 1 ) ^{2}}

\int x^{- \frac{2}{3}} d x

y^{^{'}} = \frac{( x ^{2} + y )}{x ^{3}}

x \to 0 lim (x^{2} csc^{2} (2 x))

What is the derivative of (e^{-x}-e^5(e^x+e^{-2})) ?
The derivative of (e^{-x}-e^5(e^x+e^{-2})) is -e^{-x-2}-e^{x+5}
What is the first derivative of (e^{-x}-e^5(e^x+e^{-2})) ?
The first derivative of (e^{-x}-e^5(e^x+e^{-2})) is -e^{-x-2}-e^{x+5}