What is the derivative of y=sqrt(1+e^x) ?

The derivative of y=sqrt(1+e^x) is (e^x)/(2sqrt(1+e^x))

What is the first derivative of y=sqrt(1+e^x) ?

The first derivative of y=sqrt(1+e^x) is (e^x)/(2sqrt(1+e^x))

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derivative of

y = 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}}

- \frac{2 x}{( x ^{2} + 1 ) ^{2}}

y^{^{''}} + 2 y^{^{'}} + \frac{3}{4} y = \frac{3}{4}

\int x^{3} cos (2 x) d x

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

\int (6 e^{5 x} - \frac{7}{x}) d x

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