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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 3500(1-1/50 x^2)

\frac{d}{d x} (3500 (1 - \frac{1}{50} x)^{2})

integral of (5x+3)

\int (5 x + 3) d x

yln(x)(xdy+ydx)=(xyln(x)-y)dy

y ln (x) (x d y + y d x) = (x y ln (x) - y) d y

integral of (2x-1)e^{-x}

\int (2 x - 1) e^{- x} d x

tangent of f(x)=(6x-2)^{1/3},\at x=1 tangent of

f (x) = (6 x - 2)^{\frac{1}{3}}, at x = 1

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))