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

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

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

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

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

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

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

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

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

Simplify

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

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

\int 4 e^{- \frac{x}{4}} d x

f (x) = - 2 sin (x)

\frac{5 + 5 ^{2} + 4 x ^{2}}{2}

e^{x} + 17

\frac{d}{d x} (ln (\frac{cos ( x )}{sin ( x )}))

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