What is the derivative of ln(1+9x) ?

The derivative of ln(1+9x) is 9/(1+9x)

What is the first derivative of ln(1+9x) ?

The first derivative of ln(1+9x) is 9/(1+9x)

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\frac{d}{d x} (ln (1 + 9 x))

\frac{9}{1 + 9 x}

Solution steps

\frac{d}{d x} (ln (1 + 9 x))

Apply the chain rule:

\frac{1}{1 + 9 x} \frac{d}{d x} (1 + 9 x)

= \frac{1}{1 + 9 x} \frac{d}{d x} (1 + 9 x)

\frac{d}{d x} (1 + 9 x) = 9

= \frac{1}{1 + 9 x} \cdot 9

Simplify

\frac{1}{1 + 9 x} \cdot 9 : \frac{9}{1 + 9 x}

= \frac{9}{1 + 9 x}

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

\int \frac{1}{x ^{2} - 9} d x

\int \frac{4 e ^{3 x}}{1 + e ^{3 x}} d x

x \to 0 lim (1 + 3^{x})

\int x^{2} x^{3} + 7 d x

What is the derivative of ln(1+9x) ?
The derivative of ln(1+9x) is 9/(1+9x)
What is the first derivative of ln(1+9x) ?
The first derivative of ln(1+9x) is 9/(1+9x)