What is the derivative of f(x)= x/(7-sqrt(x)) ?

The derivative of f(x)= x/(7-sqrt(x)) is (14-sqrt(x))/(2(7-sqrt(x))^2)

What is the first derivative of f(x)= x/(7-sqrt(x)) ?

The first derivative of f(x)= x/(7-sqrt(x)) is (14-sqrt(x))/(2(7-sqrt(x))^2)

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derivative of

f (x) = \frac{x}{7 - x}

\frac{14 - x}{2 ( 7 - x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{7 - x})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 7 - x ) - \frac{d}{d x} ( 7 - x ) x}{( 7 - x ) ^{2}}

\frac{d x}{d x} = 1

\frac{d}{d x} (7 - x) = - \frac{1}{2 x}

= \frac{1 \cdot ( 7 - x ) - ( - \frac{1}{2 x} ) x}{( 7 - x ) ^{2}}

Simplify

\frac{1 \cdot ( 7 - x ) - ( - \frac{1}{2 x} ) x}{( 7 - x ) ^{2}} : \frac{14 - x}{2 ( 7 - x ) ^{2}}

= \frac{14 - x}{2 ( 7 - x ) ^{2}}

What is the derivative of f(x)= x/(7-sqrt(x)) ?
The derivative of f(x)= x/(7-sqrt(x)) is (14-sqrt(x))/(2(7-sqrt(x))^2)
What is the first derivative of f(x)= x/(7-sqrt(x)) ?
The first derivative of f(x)= x/(7-sqrt(x)) is (14-sqrt(x))/(2(7-sqrt(x))^2)