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

The derivative of ((x-1))/((sqrt(x+1))) is (x+3)/(2(x+1)sqrt(x+1))

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

The first derivative of ((x-1))/((sqrt(x+1))) is (x+3)/(2(x+1)sqrt(x+1))

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derivative of

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

\frac{x + 3}{2 ( x + 1 ) x + 1}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{1 \cdot x + 1 - \frac{1}{2 x + 1} ( x - 1 )}{( x + 1 ) ^{2}} : \frac{x + 3}{2 ( x + 1 ) x + 1}

= \frac{x + 3}{2 ( x + 1 ) x + 1}

2 + x^{2}

lo g_{10} (x^{2})

\frac{d}{d t} (15 + 4 t)

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

\frac{d}{d t} (2 + 1 t + 5 t^{2})

What is the derivative of ((x-1))/((sqrt(x+1))) ?
The derivative of ((x-1))/((sqrt(x+1))) is (x+3)/(2(x+1)sqrt(x+1))
What is the first derivative of ((x-1))/((sqrt(x+1))) ?
The first derivative of ((x-1))/((sqrt(x+1))) is (x+3)/(2(x+1)sqrt(x+1))