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

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

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

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

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

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

Solution steps

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

Apply log rule:

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

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

Take the constant out:

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

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

Simplify

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

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

7 x^{2}

(x^{4})^{^{'}}

\frac{\partial}{\partial x} (\frac{1}{2} y arctan (\frac{x}{y}))

\int \frac{x ^{2} - 3 x - 7}{( 2 x + 3 ) ( x + 1 )} d x

\int_{1}^{e^{3}} \frac{1}{x ( 1 + ln ( x ) )} d x

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