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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{d}{d x} (x^{3} sin (5 x))

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

2 y = 5 x, y = 4, 2 y + 3 x = 8

\int (1 + x + x^{2}) ln (x) d x

y = - csc (x) - sin (x)

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