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

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

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

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

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

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

Solution steps

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

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

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

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

Simplify

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

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

\frac{d}{d x} (2 x + \frac{18}{x} + 1)

\int (2 x^{\frac{1}{2}}) d x

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

\int_{1}^{100} x d x

y^{^{''}} - (\frac{6}{x}) y^{^{'}} - (\frac{8}{x ^{2}}) y = 0

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