What is the derivative of ln(xe^{sqrt(x)}+2) ?

The derivative of ln(xe^{sqrt(x)}+2) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+2)}

What is the first derivative of ln(xe^{sqrt(x)}+2) ?

The first derivative of ln(xe^{sqrt(x)}+2) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+2)}

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derivative of

ln (x e^{x} + 2)

\frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 2 )}

Solution steps

\frac{d}{d x} (ln (x e^{x} + 2))

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 2 )}

\frac{d}{d x} (\frac{2 cot ( x )}{csc ( x )})

\frac{d}{d x} (I n (- x^{2} + 6 x))

x \to 1 + lim (\frac{x + 9}{x + 2})

\frac{\partial}{\partial x} (4 y x^{3} - 12 y^{2} x^{2})

s e^{- s}

What is the derivative of ln(xe^{sqrt(x)}+2) ?
The derivative of ln(xe^{sqrt(x)}+2) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+2)}
What is the first derivative of ln(xe^{sqrt(x)}+2) ?
The first derivative of ln(xe^{sqrt(x)}+2) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+2)}