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

The derivative of (ln(x)/(ln(x)+2)) is 2/(x(ln(x)+2)^2)

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

The first derivative of (ln(x)/(ln(x)+2)) is 2/(x(ln(x)+2)^2)

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

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

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

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

Simplify

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

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

\frac{d}{d x} (5 x^{4} - 2 x^{3} - x^{2})

\int 16 sin^{2} (x) d x

\int 3 x d x

\frac{\partial}{\partial φ} (sin (θ) cos (φ))

\int 1 + 16 x^{2} d x

What is the derivative of (ln(x)/(ln(x)+2)) ?
The derivative of (ln(x)/(ln(x)+2)) is 2/(x(ln(x)+2)^2)
What is the first derivative of (ln(x)/(ln(x)+2)) ?
The first derivative of (ln(x)/(ln(x)+2)) is 2/(x(ln(x)+2)^2)