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Popular >

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

Solution

derivative of

\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

(dy)/(dx)= 1/(xy+x+y+1)

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

derivative of csc(7x)

\frac{d}{d x} (csc (7 x))

integral of (e^{2x}-5x)^2

\int (e^{2 x} - 5 x)^{2} d x

derivative of (2x-1)^2ln(2x-1)derivative of

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

integral of (x^2-7)^2(2x)

\int (x^{2} - 7)^{2} (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))