What is the derivative of ln(e^x+3) ?

The derivative of ln(e^x+3) is (e^x)/(e^x+3)

What is the first derivative of ln(e^x+3) ?

The first derivative of ln(e^x+3) is (e^x)/(e^x+3)

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

\frac{e ^{x}}{e ^{x} + 3}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{e ^{x} + 3} e^{x}

Simplify

\frac{1}{e ^{x} + 3} e^{x} : \frac{e ^{x}}{e ^{x} + 3}

= \frac{e ^{x}}{e ^{x} + 3}

What is the derivative of ln(e^x+3) ?
The derivative of ln(e^x+3) is (e^x)/(e^x+3)
What is the first derivative of ln(e^x+3) ?
The first derivative of ln(e^x+3) is (e^x)/(e^x+3)