What is the derivative of ln(xe^{sqrt(x)}+4) ?

The derivative of ln(xe^{sqrt(x)}+4) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+4)}

What is the first derivative of ln(xe^{sqrt(x)}+4) ?

The first derivative of ln(xe^{sqrt(x)}+4) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+4)}

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derivative of

ln (x e^{x} + 4)

\frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 4 )}

Solution steps

\frac{d}{d x} (ln (x e^{x} + 4))

Apply the chain rule:

\frac{1}{x e ^{x} + 4} \frac{d}{d x} (x e^{x} + 4)

= \frac{1}{x e ^{x} + 4} \frac{d}{d x} (x e^{x} + 4)

\frac{d}{d x} (x e^{x} + 4) = \frac{e ^{x} x}{2} + e^{x}

= \frac{1}{x e ^{x} + 4} (\frac{e ^{x} x}{2} + e^{x})

Simplify

\frac{1}{x e ^{x} + 4} (\frac{e ^{x} x}{2} + e^{x}) : \frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 4 )}

= \frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 4 )}

\frac{d ^{2} y}{d x ^{2}} - 2 \frac{d y}{d x} + y = 2 e^{x}

x \to \infty lim (x sin (\frac{3 π}{x}))

\int_{1}^{4} y ln (y) d y

\frac{d x}{d t} = k x (1000 - x)

y^{^{''}} + 400 y = sec (20 x), y (0) = 5, y^{^{'}} (0) = - 5

What is the derivative of ln(xe^{sqrt(x)}+4) ?
The derivative of ln(xe^{sqrt(x)}+4) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+4)}
What is the first derivative of ln(xe^{sqrt(x)}+4) ?
The first derivative of ln(xe^{sqrt(x)}+4) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+4)}