What is the derivative of log_{3}(x+2) ?

The derivative of log_{3}(x+2) is 1/(ln(3)(x+2))

What is the first derivative of log_{3}(x+2) ?

The first derivative of log_{3}(x+2) is 1/(ln(3)(x+2))

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\frac{d}{d x} (lo g_{3} (x + 2))

\frac{1}{ln ( 3 ) ( x + 2 )}

Solution steps

\frac{d}{d x} (lo g_{3} (x + 2))

Apply log rule:

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

= \frac{d}{d x} (\frac{ln ( x + 2 )}{ln ( 3 )})

Take the constant out:

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

= \frac{1}{ln ( 3 )} \frac{d}{d x} (ln (x + 2))

Apply the chain rule:

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

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

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

= \frac{1}{ln ( 3 )} \cdot \frac{1}{x + 2} \cdot 1

Simplify

\frac{1}{ln ( 3 )} \cdot \frac{1}{x + 2} \cdot 1 : \frac{1}{ln ( 3 ) ( x + 2 )}

= \frac{1}{ln ( 3 ) ( x + 2 )}

y^{^{'}} = \frac{1}{e ^{- y} - x}

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

\frac{7}{1 - t}

\frac{\partial}{\partial x} (t e^{- t})

\frac{\partial}{\partial x} (2 x^{2} - 8 x + y^{2} - 8 y + 7)

What is the derivative of log_{3}(x+2) ?
The derivative of log_{3}(x+2) is 1/(ln(3)(x+2))
What is the first derivative of log_{3}(x+2) ?
The first derivative of log_{3}(x+2) is 1/(ln(3)(x+2))