What is the derivative of 1/2 ln((x+1/(x+3))) ?

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

Apply the chain rule:

\frac{1}{\frac{x + 1}{x + 3}} \frac{d}{d x} (\frac{x + 1}{x + 3})

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

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

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

Simplify

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

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

\frac{\partial}{\partial x} (\frac{x y ^{2}}{z})

y = x^{2} ln (2 x + 1)

\int_{1}^{e} 6 x^{2} ln (x) d x

\frac{d}{d x} (\frac{1}{( x + 1 ) ^{3} ( 3 x - 1 ) ^{2}})

\frac{d}{d x} ((\frac{x}{2})^{4})

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