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Popular >

derivative of ln(1+2/x)

Solution

\frac{d}{d x} (ln (1 + \frac{2}{x}))

Solution

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

Solution steps

\frac{d}{d x} (ln (1 + \frac{2}{x}))

Apply the chain rule:

\frac{1}{1 + \frac{2}{x}} \frac{d}{d x} (1 + \frac{2}{x})

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

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

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

Simplify

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

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

Popular Examples

integral from-1 to 5 of (8y)/(y^2-4y-12)

\int_{- 1}^{5} \frac{8 y}{y ^{2} - 4 y - 12} d y

integral of 16csc(8x)sec(8x)

\int 16 csc (8 x) sec (8 x) d x

area x^2+2x+1,-1,7 area

x^{2} + 2 x + 1, - 1, 7

area y=8x,y=x^2-9 area

y = 8 x, y = x^{2} - 9

derivative of (400/(1+39e^{-0.16x)})

\frac{d}{d x} (\frac{400}{1 + 39 e ^{- 0.16 x}})

Frequently Asked Questions (FAQ)

What is the derivative of ln(1+2/x) ?
The derivative of ln(1+2/x) is -2/(x(x+2))
What is the first derivative of ln(1+2/x) ?
The first derivative of ln(1+2/x) is -2/(x(x+2))