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Popular >

derivative of ln((x+b/x))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

y^{^{'}} + 8 y = 5

integral of (3x^4+4)/(x^2(x^2+1)^3)

\int \frac{3 x ^{4} + 4}{x ^{2} ( x ^{2} + 1 ) ^{3}} d x

area y=x^2,x=0,x=4 area

y = x^{2}, x = 0, x = 4

integral of (((x+1)))/((x^2-x-6))

\int \frac{( ( x + 1 ) )}{( x ^{2} - x - 6 )} d x

(\partial)/(\partial x)(5^{x^2})

\frac{\partial}{\partial x} (5^{x^{2}})

Frequently Asked Questions (FAQ)

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