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

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

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

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

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derivative of

\frac{x}{x + 3}

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

y^{^{''}} - y = 0, y (0) = 1, y^{^{'}} (0) = 2

y = \frac{x ^{2} - 7 x + 2}{x - 2}

\int \frac{x}{( x ^{2} + 4 ) ^{\frac{3}{2}}} d x

f (x) = x^{2} + 2, [- 2, 1]

\frac{\partial}{\partial y} (2 y - 2 x)

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