What is the derivative of ((sqrt(x)-3)/(sqrt(x)+3)) ?

The derivative of ((sqrt(x)-3)/(sqrt(x)+3)) is 3/(sqrt(x)(\sqrt{x)+3)^2}

What is the first derivative of ((sqrt(x)-3)/(sqrt(x)+3)) ?

The first derivative of ((sqrt(x)-3)/(sqrt(x)+3)) is 3/(sqrt(x)(\sqrt{x)+3)^2}

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\frac{d}{d x} (\frac{( x - 3 )}{x + 3})

\frac{3}{x ( x + 3 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{( x - 3 )}{x + 3})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x - 3 ) ( x + 3 ) - \frac{d}{d x} ( x + 3 ) ( x - 3 )}{( x + 3 ) ^{2}}

\frac{d}{d x} (x - 3) = \frac{1}{2 x}

\frac{d}{d x} (x + 3) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( x + 3 ) - \frac{1}{2 x} ( x - 3 )}{( x + 3 ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( x + 3 ) - \frac{1}{2 x} ( x - 3 )}{( x + 3 ) ^{2}} : \frac{3}{x ( x + 3 ) ^{2}}

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

\int_{0}^{4} (e^{- 0.25 x} + 5) d x

\frac{1}{( s ^{2} + 1 ) ( s ^{2} )}

x \to 0 + lim (arccot (x))

\int (2 x^{2} + 3 x - 3) (5 x + 3) d x

f (x) = \frac{x ^{4}}{8} - 8 x

What is the derivative of ((sqrt(x)-3)/(sqrt(x)+3)) ?
The derivative of ((sqrt(x)-3)/(sqrt(x)+3)) is 3/(sqrt(x)(\sqrt{x)+3)^2}
What is the first derivative of ((sqrt(x)-3)/(sqrt(x)+3)) ?
The first derivative of ((sqrt(x)-3)/(sqrt(x)+3)) is 3/(sqrt(x)(\sqrt{x)+3)^2}