What is the derivative of log_{2}(2x+1) ?

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

What is the first derivative of log_{2}(2x+1) ?

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

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\frac{d}{d x} (lo g_{2} (2 x + 1))

\frac{2}{ln ( 2 ) ( 2 x + 1 )}

Solution steps

\frac{d}{d x} (lo g_{2} (2 x + 1))

Apply log rule:

lo g_{a} (b) = \frac{ln ( b )}{ln ( a )}

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

= \frac{1}{ln ( 2 )} \cdot \frac{1}{2 x + 1} \cdot 2

Simplify

\frac{1}{ln ( 2 )} \cdot \frac{1}{2 x + 1} \cdot 2 : \frac{2}{ln ( 2 ) ( 2 x + 1 )}

= \frac{2}{ln ( 2 ) ( 2 x + 1 )}

x^{2} + 2, x + 2

6 e^{- 3 x}

\int_{- \infty}^{0} \frac{1}{4 - 6 x} d x

e^{c s c (x)}

\int \frac{1}{t ^{\frac{1}{2}}} d t

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