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}}

\int \frac{8 x ^{2} + 10}{x ^{3} + 5 x} d x

x^{3} = \frac{2 y ^{5} + 4}{5 y ^{4} y ^{^{'}}}

\int sin (16 x) cos (7 x) d x

\frac{\partial}{\partial x} (x^{7} y^{6})

\int 5 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)