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Popular >

derivative of sqrt(x/(x+2))

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

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\frac{d}{d x} (e^{x^{4}} + 7 x)

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x/(x+2)) ?
The derivative of sqrt(x/(x+2)) is 1/(sqrt(x)(x+2)^{3/2)}
What is the first derivative of sqrt(x/(x+2)) ?
The first derivative of sqrt(x/(x+2)) is 1/(sqrt(x)(x+2)^{3/2)}