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Popular >

derivative of ln(x+1/x)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Graph

Popular Examples

integral from 0 to 1 of x^8

\int_{0}^{1} x^{8} d x

integral of 7/(x^2)cos(7/x)

\int \frac{7}{x ^{2}} cos (\frac{7}{x}) d x

limit as h approaches 0 of x^2+2x+h-69

h \to 0 lim (x^{2} + 2 x + h - 69)

y^'(t)=(3+y)(1-y),y(0)=2

y^{^{'}} (t) = (3 + y) (1 - y), y (0) = 2

derivative of f(t)=2t^{-5}derivative of

f (t) = 2 t^{- 5}

Frequently Asked Questions (FAQ)

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