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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

y^{''}+2y^'-3y=0,y(0)=4,y^'(0)=1

y^{^{''}} + 2 y^{^{'}} - 3 y = 0, y (0) = 4, y^{^{'}} (0) = 1

derivative of f(x)= 9/(x-6)derivative of

f (x) = \frac{9}{x - 6}

limit as x approaches 0 of x/(sin(6x))

x \to 0 lim (\frac{x}{sin ( 6 x )})

derivative of f(x)=sin^2(e^{sin^2(x)})derivative of

f (x) = sin^{2} (e^{s i n^{2} (x)})

(\partial)/(\partial x)(3y^6sin(3x))

\frac{\partial}{\partial x} (3 y^{6} sin (3 x))

Frequently Asked Questions (FAQ)

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