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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

(dy)/(dx)=2xsqrt(x-7)

\frac{d y}{d x} = 2 x x - 7

limit as x approaches-2 of (3x)/(x+2)

x \to - 2 lim (\frac{3 x}{x + 2})

integral of 5x^{3/7}

\int 5 x^{\frac{3}{7}} d x

derivative of x^2-12 derivative of

x^{2} - 12

derivative of f(x)=((2x)/3 x+3/2 x)2 derivative of

f (x) = (\frac{2 x}{3} x + \frac{3}{2} x) 2

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))