What is the derivative of ln(5+e^{18x}) ?

The derivative of ln(5+e^{18x}) is (18e^{18x})/(5+e^{18x)}

What is the first derivative of ln(5+e^{18x}) ?

The first derivative of ln(5+e^{18x}) is (18e^{18x})/(5+e^{18x)}

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derivative of

ln (5 + e^{18 x})

\frac{18 e ^{18 x}}{5 + e ^{18 x}}

Solution steps

\frac{d}{d x} (ln (5 + e^{18 x}))

Apply the chain rule:

\frac{1}{5 + e ^{18 x}} \frac{d}{d x} (5 + e^{18 x})

= \frac{1}{5 + e ^{18 x}} \frac{d}{d x} (5 + e^{18 x})

\frac{d}{d x} (5 + e^{18 x}) = 18 e^{18 x}

= \frac{1}{5 + e ^{18 x}} \cdot 18 e^{18 x}

Simplify

\frac{1}{5 + e ^{18 x}} \cdot 18 e^{18 x} : \frac{18 e ^{18 x}}{5 + e ^{18 x}}

= \frac{18 e ^{18 x}}{5 + e ^{18 x}}

\int 5 x + \frac{1}{5 x} d x

\int x 64 x^{4} + 81 d x

\int 2 sin (y^{2}) d y

y = 4 x

\frac{S + \frac{1}{2}}{S ^{2} - 2 S + 5}

What is the derivative of ln(5+e^{18x}) ?
The derivative of ln(5+e^{18x}) is (18e^{18x})/(5+e^{18x)}
What is the first derivative of ln(5+e^{18x}) ?
The first derivative of ln(5+e^{18x}) is (18e^{18x})/(5+e^{18x)}