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Popular >

derivative of (x-1/(sqrt(x)))

Solution

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

Solution

\frac{x + 1}{2 x x}

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}{d x} ( x ) ( x - 1 )}{( x ) ^{2}}

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

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

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

Simplify

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

= \frac{x + 1}{2 x x}

Popular Examples

derivative of a/(x^3)

\frac{d}{d x} (\frac{a}{x ^{3}})

integral of 1/(cos^2(u))

\int \frac{1}{cos ^{2} ( u )} d u

(\partial)/(\partial z)(y)

\frac{\partial}{\partial z} (y)

derivative of e^{cosh(3x})

\frac{d}{d x} (e^{c o s h (3 x)})

integral of 1/(4-3sin^2(x)+5cos^2(x))

\int \frac{1}{4 - 3 sin ^{2} ( x ) + 5 cos ^{2} ( x )} d x

Frequently Asked Questions (FAQ)

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