What is the derivative of ln(xe^{sqrt(x)}+3) ?

The derivative of ln(xe^{sqrt(x)}+3) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+3)}

What is the first derivative of ln(xe^{sqrt(x)}+3) ?

The first derivative of ln(xe^{sqrt(x)}+3) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+3)}

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\frac{d}{d x} (ln (x e^{x} + 3))

\frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 3 )}

Solution steps

\frac{d}{d x} (ln (x e^{x} + 3))

Apply the chain rule:

\frac{1}{x e ^{x} + 3} \frac{d}{d x} (x e^{x} + 3)

= \frac{1}{x e ^{x} + 3} \frac{d}{d x} (x e^{x} + 3)

\frac{d}{d x} (x e^{x} + 3) = \frac{e ^{x} x}{2} + e^{x}

= \frac{1}{x e ^{x} + 3} (\frac{e ^{x} x}{2} + e^{x})

Simplify

\frac{1}{x e ^{x} + 3} (\frac{e ^{x} x}{2} + e^{x}) : \frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 3 )}

= \frac{e ^{x} x + 2 e ^{x}}{2 ( e ^{x} x + 3 )}

\frac{d}{d x} (x^{3} (x^{4} - 1))

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

\frac{s + 3}{s + 1 ( s + 2 )}

\int - 2 sin^{2} (t) d t

\frac{\partial}{\partial x} (4374 x^{\frac{1}{3}} + 2 y)

What is the derivative of ln(xe^{sqrt(x)}+3) ?
The derivative of ln(xe^{sqrt(x)}+3) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+3)}
What is the first derivative of ln(xe^{sqrt(x)}+3) ?
The first derivative of ln(xe^{sqrt(x)}+3) is (e^{sqrt(x)}sqrt(x)+2e^{sqrt(x)})/(2(e^{sqrt(x))x+3)}