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Popular >

derivative of-1/2 e^{-x/2}

Solution

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

Solution

\frac{1}{4} e^{- \frac{x}{2}}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{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}

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

Simplify

- \frac{1}{2} e^{- \frac{x}{2}} (- \frac{1}{2}) : \frac{1}{4} e^{- \frac{x}{2}}

= \frac{1}{4} e^{- \frac{x}{2}}

Popular Examples

integral of (x^2-3x+11)/((x^2-4x+10)^2)

\int \frac{x ^{2} - 3 x + 11}{( x ^{2} - 4 x + 10 ) ^{2}} d x

derivative of f(x)=(x^3)/(4-x^2)derivative of

f (x) = \frac{x ^{3}}{4 - x ^{2}}

integral of sqrt(1+u^2)

\int 1 + u^{2} d u

integral from 0 to 4 of x^3sqrt(x^2+16)

\int_{0}^{4} x^{3} x^{2} + 16 d x

derivative of 3x^2+2x+1

\frac{d}{d x} (3 x^{2} + 2 x + 1)

Frequently Asked Questions (FAQ)

What is the derivative of-1/2 e^{-x/2} ?
The derivative of-1/2 e^{-x/2} is 1/4 e^{-x/2}
What is the first derivative of-1/2 e^{-x/2} ?
The first derivative of-1/2 e^{-x/2} is 1/4 e^{-x/2}