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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

tangent of 6sqrt(x)-3x tangent of

6 x - 3 x

integral of (16x^3-4x)/(2x^4-x^2+3)

\int \frac{16 x ^{3} - 4 x}{2 x ^{4} - x ^{2} + 3} d x

limit as x approaches 0 of sin(3/x)

x \to 0 lim (sin (\frac{3}{x}))

integral of 5e^{6x}

\int 5 e^{6 x} d x

integral of (10-5x)

\int (10 - 5 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))