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Popular >

derivative of ((x+1)/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d x}{d x} = 1

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

Simplify

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

= - \frac{1}{x ^{2}}

Popular Examples

derivative of arcsin(4x)derivative of

arcsin (4 x)

integral of (x^3)/(y^2)

\int \frac{x ^{3}}{y ^{2}} d x

taylor 1/((x+1)^2)1 taylor

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

integral of x^2sqrt(9+x^2)

\int x^{2} 9 + x^{2} d x

inverse oflaplace 1/(2002s^2+9)inverse laplace

\frac{1}{2002 s ^{2} + 9}

Frequently Asked Questions (FAQ)

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