What is the derivative of log_{e}(x+1) ?

The derivative of log_{e}(x+1) is 1/(x+1)

What is the first derivative of log_{e}(x+1) ?

The first derivative of log_{e}(x+1) is 1/(x+1)

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\frac{d}{d x} (lo g_{e} (x + 1))

\frac{1}{x + 1}

Solution steps

\frac{d}{d x} (lo g_{e} (x + 1))

Simplify

lo g_{e} (x + 1) : ln (x + 1)

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

Apply the chain rule:

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

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

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

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

Simplify

= \frac{1}{x + 1}

\int \frac{1}{cos ( θ ) - 1} d θ

y^{^{'''}} - 9 y^{^{''}} + 15 y^{^{'}} + 25 y = 0

\frac{\partial}{\partial x} (\frac{x}{v})

x \to 8 + lim (\frac{∣ x - 8 ∣}{x - 8})

\frac{d}{d x} (\frac{5 x ^{3} - 7}{x})

What is the derivative of log_{e}(x+1) ?
The derivative of log_{e}(x+1) is 1/(x+1)
What is the first derivative of log_{e}(x+1) ?
The first derivative of log_{e}(x+1) is 1/(x+1)