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

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

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

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

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derivative of

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

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

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

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

Simplify

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

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

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