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

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

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

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

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

x - 6

\int ln (cos (w)) tan (w) d w

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

f (x) = (11 x + 2) x^{2}

x \to \infty lim (\frac{ln ( x ) + x ^{3}}{e ^{- x}})

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