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

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

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

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

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

\frac{- 1 + x + 1}{2 x x x + 1}

Solution steps

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

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

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

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

Simplify

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

= \frac{- 1 + x + 1}{2 x x x + 1}

\frac{d}{d x} (3 e^{x} + 5 x^{2})

3 \cdot \frac{d y}{d x} + 5 y = 1

- cos (2 x) - 2 sin (2 x) (1 - x)

cos (sin (tan (7 x)))

1, 8, [- 0.5 x + 6], x + 2

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