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}}

y = 6 cos (x) + 3 sin (2 x)

\frac{d}{d x} (\frac{8 x ^{2} + 8 x + 2}{x})

\int \frac{4}{x ^{2} 16 - x ^{2}} d x

(x + 2)^{2} + (y - 3)^{2} = 37, (4, 4)

\int \frac{x}{1} d x

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)