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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

(\partial)/(\partial x)(x^3-3xy)

\frac{\partial}{\partial x} (x^{3} - 3 x y)

(\partial)/(\partial y)(3x+5y-1)

\frac{\partial}{\partial y} (3 x + 5 y - 1)

derivative of ln(x^2sqrt(x^2+1))

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

(dy}{dx}=\frac{(6xsec(y/x)+y))/x

\frac{d y}{d x} = \frac{( 6 x sec ( \frac{y}{x} ) + y )}{x}

taylor cos(x)+1/x , pi/2 taylor

cos (x) + \frac{1}{x}, \frac{π}{2}

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)