What is the derivative of f(x)=(sqrt(x))/(5+x) ?

The derivative of f(x)=(sqrt(x))/(5+x) is (5-x)/(2sqrt(x)(5+x)^2)

What is the first derivative of f(x)=(sqrt(x))/(5+x) ?

The first derivative of f(x)=(sqrt(x))/(5+x) is (5-x)/(2sqrt(x)(5+x)^2)

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derivative of

f (x) = \frac{x}{5 + x}

\frac{5 - x}{2 x ( 5 + x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{5 + x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ) ( 5 + x ) - \frac{d}{d x} ( 5 + x ) x}{( 5 + x ) ^{2}}

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

\frac{d}{d x} (5 + x) = 1

= \frac{\frac{1}{2 x} ( 5 + x ) - 1 \cdot x}{( 5 + x ) ^{2}}

Simplify

\frac{\frac{1}{2 x} ( 5 + x ) - 1 \cdot x}{( 5 + x ) ^{2}} : \frac{5 - x}{2 x ( 5 + x ) ^{2}}

= \frac{5 - x}{2 x ( 5 + x ) ^{2}}

f (x) = \frac{x}{x + 1}, at x = 4

2 s

2 x d y + (x^{2} y^{4} + 1) y d x = 0

\int 2 cos (n x) d x

(\frac{x ^{2} + 4}{x ^{2} - 4})^{2}

What is the derivative of f(x)=(sqrt(x))/(5+x) ?
The derivative of f(x)=(sqrt(x))/(5+x) is (5-x)/(2sqrt(x)(5+x)^2)
What is the first derivative of f(x)=(sqrt(x))/(5+x) ?
The first derivative of f(x)=(sqrt(x))/(5+x) is (5-x)/(2sqrt(x)(5+x)^2)