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Popular >

derivative of ln(1+5/x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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t \to \frac{π}{3} lim (cos (t) + 2)

limit as t approaches 0 of (2t)/(tan(t))

t \to 0 lim (\frac{2 t}{tan ( t )})

y^'=6e^{(2x-y)},y(0)=0

y^{^{'}} = 6 e^{(2 x - y)}, y (0) = 0

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\int \frac{( 1 + e ^{x} ) ^{2}}{e ^{x}} d x

Frequently Asked Questions (FAQ)

What is the derivative of ln(1+5/x) ?
The derivative of ln(1+5/x) is -5/(x(x+5))
What is the first derivative of ln(1+5/x) ?
The first derivative of ln(1+5/x) is -5/(x(x+5))