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Popular >

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

Solution

derivative of

\frac{2 x + 5}{x}

Solution

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

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}{d x} ( x ) ( 2 x + 5 )}{( x ) ^{2}}

\frac{d}{d x} (2 x + 5) = 2

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

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

Simplify

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

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

Popular Examples

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\frac{d}{d x} (\frac{x ^{3}}{f ( x )})

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\int \frac{9}{t ^{2}} d t

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\int sec (θ) (sec (θ) + tan (θ)) d θ

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x \to 0 lim (\frac{x}{sin ( 12 x )})

integral of (60)/(2x+5)-4

\int \frac{60}{2 x + 5} - 4 d x

Frequently Asked Questions (FAQ)

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