What is the derivative of f(x)=sqrt(x/(x+9)) ?

The derivative of f(x)=sqrt(x/(x+9)) is 9/(2sqrt(x)(x+9)^{3/2)}

What is the first derivative of f(x)=sqrt(x/(x+9)) ?

The first derivative of f(x)=sqrt(x/(x+9)) is 9/(2sqrt(x)(x+9)^{3/2)}

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derivative of

f (x) = \frac{x}{x + 9}

\frac{9}{2 x ( x + 9 ) ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{x}{x + 9})

Apply the chain rule:

\frac{1}{2 \frac{x}{x + 9}} \frac{d}{d x} (\frac{x}{x + 9})

= \frac{1}{2 \frac{x}{x + 9}} \frac{d}{d x} (\frac{x}{x + 9})

\frac{d}{d x} (\frac{x}{x + 9}) = \frac{9}{( x + 9 ) ^{2}}

= \frac{1}{2 \frac{x}{x + 9}} \cdot \frac{9}{( x + 9 ) ^{2}}

Simplify

\frac{1}{2 \frac{x}{x + 9}} \cdot \frac{9}{( x + 9 ) ^{2}} : \frac{9}{2 x ( x + 9 ) ^{\frac{3}{2}}}

= \frac{9}{2 x ( x + 9 ) ^{\frac{3}{2}}}

What is the derivative of f(x)=sqrt(x/(x+9)) ?
The derivative of f(x)=sqrt(x/(x+9)) is 9/(2sqrt(x)(x+9)^{3/2)}
What is the first derivative of f(x)=sqrt(x/(x+9)) ?
The first derivative of f(x)=sqrt(x/(x+9)) is 9/(2sqrt(x)(x+9)^{3/2)}