What is the derivative of ((sqrt(x)-2))/(sqrt(x)+3) ?

The derivative of ((sqrt(x)-2))/(sqrt(x)+3) is 5/(2sqrt(x)(\sqrt{x)+3)^2}

What is the first derivative of ((sqrt(x)-2))/(sqrt(x)+3) ?

The first derivative of ((sqrt(x)-2))/(sqrt(x)+3) is 5/(2sqrt(x)(\sqrt{x)+3)^2}

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derivative of

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

\frac{5}{2 x ( x + 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

Simplify

\frac{\frac{1}{2 x} ( x + 3 ) - \frac{1}{2 x} ( x - 2 )}{( x + 3 ) ^{2}} : \frac{5}{2 x ( x + 3 ) ^{2}}

= \frac{5}{2 x ( x + 3 ) ^{2}}

\frac{d}{d x} (3 x y)

\frac{2 x}{( x ^{2} + 4 ) ^{2}}

\frac{d}{d x} (ln (arctan (8 x^{5})))

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

\int 3 x \cdot (x + 1)^{2} d x

What is the derivative of ((sqrt(x)-2))/(sqrt(x)+3) ?
The derivative of ((sqrt(x)-2))/(sqrt(x)+3) is 5/(2sqrt(x)(\sqrt{x)+3)^2}
What is the first derivative of ((sqrt(x)-2))/(sqrt(x)+3) ?
The first derivative of ((sqrt(x)-2))/(sqrt(x)+3) is 5/(2sqrt(x)(\sqrt{x)+3)^2}