What is the derivative of y=ln((5x)/(7+x)) ?

The derivative of y=ln((5x)/(7+x)) is 7/(x(x+7))

What is the first derivative of y=ln((5x)/(7+x)) ?

The first derivative of y=ln((5x)/(7+x)) is 7/(x(x+7))

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derivative of

y = ln (\frac{5 x}{7 + x})

\frac{7}{x ( x + 7 )}

Solution steps

\frac{d}{d x} (ln (\frac{5 x}{7 + x}))

Apply the chain rule:

\frac{1}{\frac{5 x}{7 + x}} \frac{d}{d x} (\frac{5 x}{7 + x})

= \frac{1}{\frac{5 x}{7 + x}} \frac{d}{d x} (\frac{5 x}{7 + x})

\frac{d}{d x} (\frac{5 x}{7 + x}) = \frac{35}{( 7 + x ) ^{2}}

= \frac{1}{\frac{5 x}{7 + x}} \cdot \frac{35}{( 7 + x ) ^{2}}

Simplify

\frac{1}{\frac{5 x}{7 + x}} \cdot \frac{35}{( 7 + x ) ^{2}} : \frac{7}{x ( x + 7 )}

= \frac{7}{x ( x + 7 )}

What is the derivative of y=ln((5x)/(7+x)) ?
The derivative of y=ln((5x)/(7+x)) is 7/(x(x+7))
What is the first derivative of y=ln((5x)/(7+x)) ?
The first derivative of y=ln((5x)/(7+x)) is 7/(x(x+7))