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Popular >

derivative of ln(1+4/x)

Solution

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

Solution

- \frac{4}{x ( x + 4 )}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (1 + \frac{4}{x}) = - \frac{4}{x ^{2}}

= \frac{1}{1 + \frac{4}{x}} (- \frac{4}{x ^{2}})

Simplify

\frac{1}{1 + \frac{4}{x}} (- \frac{4}{x ^{2}}) : - \frac{4}{x ( x + 4 )}

= - \frac{4}{x ( x + 4 )}

Popular Examples

y^{^{'}} = (y^{2} - 1) x

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\frac{d}{d x} (\frac{x ^{2} + 3}{x ^{2} - 9 x})

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(\partial)/(\partial u)(u*sin(v))

\frac{\partial}{\partial u} (u \cdot sin (v))

integral from-2 to 1 of 1/(sqrt(2-x))

\int_{- 2}^{1} \frac{1}{2 - x} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(1+4/x) ?
The derivative of ln(1+4/x) is -4/(x(x+4))
What is the first derivative of ln(1+4/x) ?
The first derivative of ln(1+4/x) is -4/(x(x+4))