What is the derivative of ln(e^x+2) ?

The derivative of ln(e^x+2) is (e^x)/(e^x+2)

What is the first derivative of ln(e^x+2) ?

The first derivative of ln(e^x+2) is (e^x)/(e^x+2)

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derivative of

ln (e^{x} + 2)

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

(\frac{t ^{2}}{( t ^{3} + 2 )})^{2}

3 x^{3} - 2 x^{2} - x + 1

(2 x - 3)^{\frac{5}{2}}

(a - x)^{- 2}

cot (3 x^{5})

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