What is the derivative of x/(1+sqrt(x)) ?

The derivative of x/(1+sqrt(x)) is (2+sqrt(x))/(2(1+sqrt(x))^2)

What is the first derivative of x/(1+sqrt(x)) ?

The first derivative of x/(1+sqrt(x)) is (2+sqrt(x))/(2(1+sqrt(x))^2)

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

n = 4 \sum \infty \frac{1}{n ^{4}}

y = 2 x e^{x}, (0, 0)

\frac{d y}{d x} = 7 y

\int sin (ln (x^{2})) d x

(5 x^{2} + 3 y + 3 y^{2}) d x + (x + 2 x y) d y = 0

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