What is the derivative of 1/(In(x+2)) ?

The derivative of 1/(In(x+2)) is -1/(nI(x+2)^2)

What is the first derivative of 1/(In(x+2)) ?

The first derivative of 1/(In(x+2)) is -1/(nI(x+2)^2)

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

- \frac{1}{n I ( x + 2 ) ^{2}}

Solution steps

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

Treat

n, I

as a constant

Take the constant out:

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

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

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{1}{I n} \frac{d}{d x} ((x + 2)^{- 1})

Apply the chain rule:

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

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

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

= \frac{1}{I n} (- \frac{1}{( x + 2 ) ^{2}} \cdot 1)

Simplify

\frac{1}{I n} (- \frac{1}{( x + 2 ) ^{2}} \cdot 1) : - \frac{1}{n I ( x + 2 ) ^{2}}

= - \frac{1}{n I ( x + 2 ) ^{2}}

What is the derivative of 1/(In(x+2)) ?
The derivative of 1/(In(x+2)) is -1/(nI(x+2)^2)
What is the first derivative of 1/(In(x+2)) ?
The first derivative of 1/(In(x+2)) is -1/(nI(x+2)^2)