What is the derivative of (-4x-4sqrt(1+x)/(x^2-1)) ?

The derivative of (-4x-4sqrt(1+x)/(x^2-1)) is (4x^2+6xsqrt(x+1)+2sqrt(x+1)+4)/((x^2-1)^2)

What is the first derivative of (-4x-4sqrt(1+x)/(x^2-1)) ?

The first derivative of (-4x-4sqrt(1+x)/(x^2-1)) is (4x^2+6xsqrt(x+1)+2sqrt(x+1)+4)/((x^2-1)^2)

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\frac{d}{d x} (\frac{- 4 x - 4 1 + x}{x ^{2} - 1})

\frac{4 x ^{2} + 6 x x + 1 + 2 x + 1 + 4}{( x ^{2} - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{- 4 x - 4 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} ( - 4 x - 4 1 + x ) ( x ^{2} - 1 ) - \frac{d}{d x} ( x ^{2} - 1 ) ( - 4 x - 4 1 + x )}{( x ^{2} - 1 ) ^{2}}

\frac{d}{d x} (- 4 x - 4 1 + x) = - 4 - \frac{2}{1 + x}

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

= \frac{( - 4 - \frac{2}{1 + x} ) ( x ^{2} - 1 ) - 2 x ( - 4 x - 4 1 + x )}{( x ^{2} - 1 ) ^{2}}

Expand

(- 4 - \frac{2}{1 + x}) (x^{2} - 1) - 2 x (- 4 x - 4 1 + x) : 4 x^{2} + 6 x x + 1 + 2 x + 1 + 4

= \frac{4 x ^{2} + 6 x x + 1 + 2 x + 1 + 4}{( x ^{2} - 1 ) ^{2}}

2 \frac{d y}{d x} - \frac{( 45 x ^{4} )}{y} = 0

f (x) = x + 4

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

\int \frac{4 x ^{6} + 3 x ^{5} - 8}{x ^{5}} d x

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

What is the derivative of (-4x-4sqrt(1+x)/(x^2-1)) ?
The derivative of (-4x-4sqrt(1+x)/(x^2-1)) is (4x^2+6xsqrt(x+1)+2sqrt(x+1)+4)/((x^2-1)^2)
What is the first derivative of (-4x-4sqrt(1+x)/(x^2-1)) ?
The first derivative of (-4x-4sqrt(1+x)/(x^2-1)) is (4x^2+6xsqrt(x+1)+2sqrt(x+1)+4)/((x^2-1)^2)