What is the derivative of sqrt(1-e^x) ?

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

What is the first derivative of sqrt(1-e^x) ?

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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