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

The derivative derivative of e^{(-x/2}) is -1/2 e^{-x/2}

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

The first derivative derivative of e^{(-x/2}) is -1/2 e^{-x/2}

derivative of

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

- \frac{1}{2} e^{- \frac{x}{2}}

Solution steps

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

Simplify

e^{\frac{- x}{2}} : e^{- \frac{x}{2}}

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

Apply the chain rule:

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

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

\frac{d}{d x} (- \frac{x}{2}) = - \frac{1}{2}

= e^{- \frac{x}{2}} (- \frac{1}{2})

Simplify

= - \frac{1}{2} e^{- \frac{x}{2}}

f (x) = sin (x)

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

\frac{d}{d x} (\frac{( d ^{2} y ( d , x ) )}{( d x ^{2} )})

\int (sec (θ)) d θ

\frac{d}{d x} y = csc^{2} (x)

What is the derivative derivative of e^{(-x/2}) ?
The derivative derivative of e^{(-x/2}) is -1/2 e^{-x/2}
What is the first derivative derivative of e^{(-x/2}) ?
The first derivative derivative of e^{(-x/2}) is -1/2 e^{-x/2}