What is the derivative of 20(1-e^{-x/2}) ?

The derivative of 20(1-e^{-x/2}) is 10e^{-x/2}

What is the first derivative of 20(1-e^{-x/2}) ?

The first derivative of 20(1-e^{-x/2}) is 10e^{-x/2}

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\frac{d}{d x} (20 (1 - e^{- \frac{x}{2}}))

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

Solution steps

\frac{d}{d x} (20 (1 - e^{- \frac{x}{2}}))

Take the constant out:

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

= 20 \frac{d}{d x} (1 - e^{- \frac{x}{2}})

Apply the Sum/Difference Rule:

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

= 20 (\frac{d}{d x} (1) - \frac{d}{d x} (e^{- \frac{x}{2}}))

\frac{d}{d x} (1) = 0

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

= 20 (0 - (- \frac{1}{2} e^{- \frac{x}{2}}))

Simplify

20 (0 - (- \frac{1}{2} e^{- \frac{x}{2}})) : 10 e^{- \frac{x}{2}}

= 10 e^{- \frac{x}{2}}

\int - 3 x^{2} + 100 d x

\frac{\partial}{\partial x} (\frac{x ^{2}}{x - 2 y})

4 x y \frac{d y}{d x} = 3

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

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

What is the derivative of 20(1-e^{-x/2}) ?
The derivative of 20(1-e^{-x/2}) is 10e^{-x/2}
What is the first derivative of 20(1-e^{-x/2}) ?
The first derivative of 20(1-e^{-x/2}) is 10e^{-x/2}