What is the derivative of ln(xe^{sqrt(x)}+8) ?

The derivative of ln(xe^{sqrt(x)}+8) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+8)}

What is the first derivative of ln(xe^{sqrt(x)}+8) ?

The first derivative of ln(xe^{sqrt(x)}+8) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+8)}

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derivative of

ln (x e^{x} + 8)

\frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 8 )}

Solution steps

\frac{d}{d x} (ln (x e^{x} + 8))

Apply the chain rule:

\frac{1}{x e ^{x} + 8} \frac{d}{d x} (x e^{x} + 8)

= \frac{1}{x e ^{x} + 8} \frac{d}{d x} (x e^{x} + 8)

\frac{d}{d x} (x e^{x} + 8) = \frac{e ^{x} x}{2} + e^{x}

= \frac{1}{x e ^{x} + 8} (\frac{e ^{x} x}{2} + e^{x})

Simplify

\frac{1}{x e ^{x} + 8} (\frac{e ^{x} x}{2} + e^{x}) : \frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 8 )}

= \frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 8 )}

f (x) = 4 (100)^{7}

\int x^{3} - \frac{1}{2} d x

f (x) = - \frac{1}{( x - 5 ) ^{2}}, at x = - 3

\int x \cdot cos (\frac{π x}{2}) d x

\frac{d}{d x} (arccos (\frac{x}{7}))

What is the derivative of ln(xe^{sqrt(x)}+8) ?
The derivative of ln(xe^{sqrt(x)}+8) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+8)}
What is the first derivative of ln(xe^{sqrt(x)}+8) ?
The first derivative of ln(xe^{sqrt(x)}+8) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+8)}