What is the derivative of ln((4x)/(x+7)) ?

The derivative of ln((4x)/(x+7)) is 7/(x(x+7))

What is the first derivative of ln((4x)/(x+7)) ?

The first derivative of ln((4x)/(x+7)) is 7/(x(x+7))

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derivative of

ln (\frac{4 x}{x + 7})

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

Solution steps

\frac{d}{d x} (ln (\frac{4 x}{x + 7}))

Apply the chain rule:

\frac{1}{\frac{4 x}{x + 7}} \frac{d}{d x} (\frac{4 x}{x + 7})

= \frac{1}{\frac{4 x}{x + 7}} \frac{d}{d x} (\frac{4 x}{x + 7})

\frac{d}{d x} (\frac{4 x}{x + 7}) = \frac{28}{( x + 7 ) ^{2}}

= \frac{1}{\frac{4 x}{x + 7}} \cdot \frac{28}{( x + 7 ) ^{2}}

Simplify

\frac{1}{\frac{4 x}{x + 7}} \cdot \frac{28}{( x + 7 ) ^{2}} : \frac{7}{x ( x + 7 )}

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

\int \frac{( e ^{x} )}{e ^{2 x} + 3} d x

\int_{0}^{1} x x^{2} + 2 d x

2 \frac{d y}{d x} + y = 0

y = x^{m x}

\frac{\partial}{\partial x} (y^{2} + 2 e^{x^{2}} x y)

What is the derivative of ln((4x)/(x+7)) ?
The derivative of ln((4x)/(x+7)) is 7/(x(x+7))
What is the first derivative of ln((4x)/(x+7)) ?
The first derivative of ln((4x)/(x+7)) is 7/(x(x+7))