What is the derivative of ln(xe^{sqrt(x)}+7) ?

The derivative of ln(xe^{sqrt(x)}+7) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+7)}

What is the first derivative of ln(xe^{sqrt(x)}+7) ?

The first derivative of ln(xe^{sqrt(x)}+7) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+7)}

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\frac{d}{d x} (ln (x e^{x} + 7))

\frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 7 )}

Solution steps

\frac{d}{d x} (ln (x e^{x} + 7))

Apply the chain rule:

\frac{1}{x e ^{x} + 7} \frac{d}{d x} (x e^{x} + 7)

= \frac{1}{x e ^{x} + 7} \frac{d}{d x} (x e^{x} + 7)

\frac{d}{d x} (x e^{x} + 7) = \frac{e ^{x} x}{2} + e^{x}

= \frac{1}{x e ^{x} + 7} (\frac{e ^{x} x}{2} + e^{x})

Simplify

\frac{1}{x e ^{x} + 7} (\frac{e ^{x} x}{2} + e^{x}) : \frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 7 )}

= \frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 7 )}

\int_{0}^{2} \frac{1}{( x - 1 ) ^{\frac{1}{3}}} d x

\frac{d}{d y} (\frac{y ^{3}}{21} + \frac{7}{4 y})

f (x) = 8 x + ln (x^{2})

\int (5 x^{3} + 6)^{4} x^{2} d x

y^{^{'}} - y = 5 t e^{2 t}, y (0) = 1

What is the derivative of ln(xe^{sqrt(x)}+7) ?
The derivative of ln(xe^{sqrt(x)}+7) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+7)}
What is the first derivative of ln(xe^{sqrt(x)}+7) ?
The first derivative of ln(xe^{sqrt(x)}+7) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+7)}