What is the derivative of (-6+sqrt(x)/(6+sqrt(x))) ?

The derivative of (-6+sqrt(x)/(6+sqrt(x))) is 6/(sqrt(x)(\sqrt{x)+6)^2}

What is the first derivative of (-6+sqrt(x)/(6+sqrt(x))) ?

The first derivative of (-6+sqrt(x)/(6+sqrt(x))) is 6/(sqrt(x)(\sqrt{x)+6)^2}

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\frac{d}{d x} (\frac{- 6 + x}{6 + x})

\frac{6}{x ( x + 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 6 + x}{6 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( - 6 + x ) ( 6 + x ) - \frac{d}{d x} ( 6 + x ) ( - 6 + x )}{( 6 + x ) ^{2}}

\frac{d}{d x} (- 6 + x) = \frac{1}{2 x}

\frac{d}{d x} (6 + x) = \frac{1}{2 x}

= \frac{\frac{1}{2 x} ( 6 + x ) - \frac{1}{2 x} ( - 6 + x )}{( 6 + x ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( 6 + x ) - \frac{1}{2 x} ( - 6 + x )}{( 6 + x ) ^{2}} : \frac{6}{x ( x + 6 ) ^{2}}

= \frac{6}{x ( x + 6 ) ^{2}}

\frac{d}{d x} (x (x^{4} + \frac{1}{x ^{2}}))

\int (x^{5} ln (x)) d x

\int_{0}^{1} \frac{2}{x ( 1 + x )} d x

f (x) = arcsin (x)

\frac{2}{4 s ^{2} - 8 s}

What is the derivative of (-6+sqrt(x)/(6+sqrt(x))) ?
The derivative of (-6+sqrt(x)/(6+sqrt(x))) is 6/(sqrt(x)(\sqrt{x)+6)^2}
What is the first derivative of (-6+sqrt(x)/(6+sqrt(x))) ?
The first derivative of (-6+sqrt(x)/(6+sqrt(x))) is 6/(sqrt(x)(\sqrt{x)+6)^2}