What is the derivative of y=ln((sqrt(x))/(5-x)) ?

The derivative of y=ln((sqrt(x))/(5-x)) is (5+x)/(2x(-x+5))

What is the first derivative of y=ln((sqrt(x))/(5-x)) ?

The first derivative of y=ln((sqrt(x))/(5-x)) is (5+x)/(2x(-x+5))

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derivative of

y = ln (\frac{x}{5 - x})

\frac{5 + x}{2 x ( - x + 5 )}

Solution steps

\frac{d}{d x} (ln (\frac{x}{5 - x}))

Apply the chain rule:

\frac{1}{\frac{x}{5 - x}} \frac{d}{d x} (\frac{x}{5 - x})

= \frac{1}{\frac{x}{5 - x}} \frac{d}{d x} (\frac{x}{5 - x})

\frac{d}{d x} (\frac{x}{5 - x}) = \frac{5 + x}{2 x ( 5 - x ) ^{2}}

= \frac{1}{\frac{x}{5 - x}} \cdot \frac{5 + x}{2 x ( 5 - x ) ^{2}}

Simplify

\frac{1}{\frac{x}{5 - x}} \cdot \frac{5 + x}{2 x ( 5 - x ) ^{2}} : \frac{5 + x}{2 x ( - x + 5 )}

= \frac{5 + x}{2 x ( - x + 5 )}

x \to \infty lim (3 - x^{2})

\frac{d}{d x} (\frac{x - 6}{x + 6})

f (θ) = 13 θ - 8 sin (θ)

\int \frac{1}{a s} d s

n = 1 \sum \infty 0. 5^{n - 1} \cdot n

What is the derivative of y=ln((sqrt(x))/(5-x)) ?
The derivative of y=ln((sqrt(x))/(5-x)) is (5+x)/(2x(-x+5))
What is the first derivative of y=ln((sqrt(x))/(5-x)) ?
The first derivative of y=ln((sqrt(x))/(5-x)) is (5+x)/(2x(-x+5))