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

The derivative of (-4x+sqrt(1+x)/(x^2-1)) is (8x^2-3xsqrt(x+1)-sqrt(x+1)+8)/(2(x^2-1)^2)

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

The first derivative of (-4x+sqrt(1+x)/(x^2-1)) is (8x^2-3xsqrt(x+1)-sqrt(x+1)+8)/(2(x^2-1)^2)

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

\frac{8 x ^{2} - 3 x x + 1 - x + 1 + 8}{2 ( x ^{2} - 1 ) ^{2}}

Solution steps

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

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

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

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

Simplify

\frac{( - 4 + \frac{1}{2 1 + x} ) ( x ^{2} - 1 ) - 2 x ( - 4 x + 1 + x )}{( x ^{2} - 1 ) ^{2}} : \frac{8 x ^{2} - 3 x x + 1 - x + 1 + 8}{2 ( x ^{2} - 1 ) ^{2}}

= \frac{8 x ^{2} - 3 x x + 1 - x + 1 + 8}{2 ( x ^{2} - 1 ) ^{2}}

y = 2^{x^{2} - 3 x + 5}, at x = 4

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

37 arctan (x)

\frac{d y}{d x}, e^{4 x} = sin (x + 5 y)

What is the derivative of (-4x+sqrt(1+x)/(x^2-1)) ?
The derivative of (-4x+sqrt(1+x)/(x^2-1)) is (8x^2-3xsqrt(x+1)-sqrt(x+1)+8)/(2(x^2-1)^2)
What is the first derivative of (-4x+sqrt(1+x)/(x^2-1)) ?
The first derivative of (-4x+sqrt(1+x)/(x^2-1)) is (8x^2-3xsqrt(x+1)-sqrt(x+1)+8)/(2(x^2-1)^2)