What is the derivative of log_{e}(2x) ?

The derivative of log_{e}(2x) is 1/x

What is the first derivative of log_{e}(2x) ?

The first derivative of log_{e}(2x) is 1/x

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\frac{d}{d x} (lo g_{e} (2 x))

\frac{1}{x}

Solution steps

\frac{d}{d x} (lo g_{e} (2 x))

Simplify

lo g_{e} (2 x) : ln (2 x)

= \frac{d}{d x} (ln (2 x))

Apply the chain rule:

\frac{1}{2 x} \frac{d}{d x} (2 x)

= \frac{1}{2 x} \frac{d}{d x} (2 x)

\frac{d}{d x} (2 x) = 2

= \frac{1}{2 x} \cdot 2

Simplify

\frac{1}{2 x} \cdot 2 : \frac{1}{x}

= \frac{1}{x}

\int - \frac{3}{x ^{2}} + 11 - 4^{x} d x

x \to - π + lim (csc (x))

(4 x - x^{2})^{3}

x \to - \infty lim (e^{x} + 2)

\int y^{2} e^{2 y} d y

What is the derivative of log_{e}(2x) ?
The derivative of log_{e}(2x) is 1/x
What is the first derivative of log_{e}(2x) ?
The first derivative of log_{e}(2x) is 1/x