What is the derivative of (2x+9)/(sqrt(x)) ?

The derivative of (2x+9)/(sqrt(x)) is (2x-9)/(2xsqrt(x))

What is the first derivative of (2x+9)/(sqrt(x)) ?

The first derivative of (2x+9)/(sqrt(x)) is (2x-9)/(2xsqrt(x))

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derivative of

\frac{2 x + 9}{x}

\frac{2 x - 9}{2 x x}

Solution steps

\frac{d}{d x} (\frac{2 x + 9}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 2 x + 9 ) x - \frac{d}{d x} ( x ) ( 2 x + 9 )}{( x ) ^{2}}

\frac{d}{d x} (2 x + 9) = 2

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

= \frac{2 x - \frac{1}{2 x} ( 2 x + 9 )}{( x ) ^{2}}

Simplify

\frac{2 x - \frac{1}{2 x} ( 2 x + 9 )}{( x ) ^{2}} : \frac{2 x - 9}{2 x x}

= \frac{2 x - 9}{2 x x}

\int \frac{y ^{3}}{( 1 - 2 y ^{4} ) ^{5}} d y

\int_{0}^{1} \frac{36}{x ^{2} - 36} d x

x \to 3 lim (\frac{x - 3}{x + 4})

n = 1 \sum \infty \frac{3 n}{5 n - 1}

x^{\frac{1}{2}}, 4

What is the derivative of (2x+9)/(sqrt(x)) ?
The derivative of (2x+9)/(sqrt(x)) is (2x-9)/(2xsqrt(x))
What is the first derivative of (2x+9)/(sqrt(x)) ?
The first derivative of (2x+9)/(sqrt(x)) is (2x-9)/(2xsqrt(x))