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Popular >

derivative of (sqrt(2x-5)/x)

Solution

\frac{d}{d x} (\frac{2 x - 5}{x})

Solution

\frac{- x + 5}{x ^{2} 2 x - 5}

Solution steps

\frac{d}{d x} (\frac{2 x - 5}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x - 5 ) x - \frac{d x}{d x} 2 x - 5}{x ^{2}}

\frac{d}{d x} (2 x - 5) = \frac{1}{2 x - 5}

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

= \frac{\frac{1}{2 x - 5} x - 1 \cdot 2 x - 5}{x ^{2}}

Simplify

\frac{\frac{1}{2 x - 5} x - 1 \cdot 2 x - 5}{x ^{2}} : \frac{- x + 5}{x ^{2} 2 x - 5}

= \frac{- x + 5}{x ^{2} 2 x - 5}

Graph

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\int x^{2} - 6 x - 27 d x

4x(dy)/(dx)=sqrt(x^2-9)

4 x \frac{d y}{d x} = x^{2} - 9

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\int_{- 1}^{1} ln (ln (x + 3)) d x

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integral from 0 to 2 of (6x^2-4x+5)

\int_{0}^{2} (6 x^{2} - 4 x + 5) d x

Frequently Asked Questions (FAQ)

What is the derivative of (sqrt(2x-5)/x) ?
The derivative of (sqrt(2x-5)/x) is (-x+5)/(x^2sqrt(2x-5))
What is the first derivative of (sqrt(2x-5)/x) ?
The first derivative of (sqrt(2x-5)/x) is (-x+5)/(x^2sqrt(2x-5))