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

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

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

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

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

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

f (x) = e^{6}

\frac{\partial}{\partial x} (ln ((x y)^{z}))

\frac{\partial}{\partial x} (x^{2} + w^{2})

x \to 0 - lim (ln (sin (x)))

n = 1 \sum \infty \frac{1}{n + 1}

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