What is the derivative of e^{-x}-e^xx ?

The derivative of e^{-x}-e^xx is -e^{-x}-e^xx-e^x

What is the first derivative of e^{-x}-e^xx ?

The first derivative of e^{-x}-e^xx is -e^{-x}-e^xx-e^x

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

- e^{- x} - e^{x} x - e^{x}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

= - e^{- x} - e^{x} x - e^{x}

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

0 \to 1 lim (e^{0})

\frac{d y}{d x} = 0.5 - x + 2 y

\int_{0}^{x} e^{- x^{2}} d x

\int \frac{2 x ^{4} + 5 x ^{3} - x}{x ^{3}} d x

What is the derivative of e^{-x}-e^xx ?
The derivative of e^{-x}-e^xx is -e^{-x}-e^xx-e^x
What is the first derivative of e^{-x}-e^xx ?
The first derivative of e^{-x}-e^xx is -e^{-x}-e^xx-e^x