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Popular >

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

Solution

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

Solution

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

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

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

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

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

Simplify

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

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

Popular Examples

integral of (2x-3)/(sqrt(1-x^2))

\int \frac{2 x - 3}{1 - x ^{2}} d x

y^{''}+y-2*cos(x)=0

y^{^{''}} + y - 2 \cdot cos (x) = 0

derivative of ln(t^2-2t+10)derivative of

ln (t^{2} - 2 t + 10)

area 1/x ,x^2,[1,e]area

\frac{1}{x}, x^{2}, [1, e]

integral of (5x)/((x-1)^3)

\int \frac{5 x}{( x - 1 ) ^{3}} d x

Frequently Asked Questions (FAQ)

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