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

The derivative of x/(sqrt(x+9)) is (sqrt(x)+18)/(2(sqrt(x)+9)^2)

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

The first derivative of x/(sqrt(x+9)) is (sqrt(x)+18)/(2(sqrt(x)+9)^2)

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

\frac{x + 18}{2 ( x + 9 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot ( x + 9 ) - \frac{1}{2 x} x}{( x + 9 ) ^{2}} : \frac{x + 18}{2 ( x + 9 ) ^{2}}

= \frac{x + 18}{2 ( x + 9 ) ^{2}}

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

(- 5, 5), (5, - 2)

x \to 0 + lim (x^{\frac{9}{x}})

f (x) = x^{2} + 9

\int csc^{2} (2 t) d t

What is the derivative of x/(sqrt(x+9)) ?
The derivative of x/(sqrt(x+9)) is (sqrt(x)+18)/(2(sqrt(x)+9)^2)
What is the first derivative of x/(sqrt(x+9)) ?
The first derivative of x/(sqrt(x+9)) is (sqrt(x)+18)/(2(sqrt(x)+9)^2)