What is the derivative of y=(x^2+1)/(x^3-1)-5x^2 ?

The derivative of y=(x^2+1)/(x^3-1)-5x^2 is (-10x^7+19x^4-3x^2-12x)/((x^3-1)^2)

What is the first derivative of y=(x^2+1)/(x^3-1)-5x^2 ?

The first derivative of y=(x^2+1)/(x^3-1)-5x^2 is (-10x^7+19x^4-3x^2-12x)/((x^3-1)^2)

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derivative of

y = \frac{x ^{2} + 1}{x ^{3} - 1} - 5 x^{2}

\frac{- 10 x ^{7} + 19 x ^{4} - 3 x ^{2} - 12 x}{( x ^{3} - 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x ^{2} + 1}{x ^{3} - 1} - 5 x^{2})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{x ^{2} + 1}{x ^{3} - 1}) - \frac{d}{d x} (5 x^{2})

\frac{d}{d x} (\frac{x ^{2} + 1}{x ^{3} - 1}) = \frac{- x ^{4} - 3 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}}

\frac{d}{d x} (5 x^{2}) = 10 x

= \frac{- x ^{4} - 3 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}} - 10 x

Simplify

\frac{- x ^{4} - 3 x ^{2} - 2 x}{( x ^{3} - 1 ) ^{2}} - 10 x : \frac{- 10 x ^{7} + 19 x ^{4} - 3 x ^{2} - 12 x}{( x ^{3} - 1 ) ^{2}}

= \frac{- 10 x ^{7} + 19 x ^{4} - 3 x ^{2} - 12 x}{( x ^{3} - 1 ) ^{2}}

\frac{e ^{x}}{1 + e ^{x}}

x^{3} + 4 y^{2} = 12, (2, - 1)

\frac{d y}{d x} = x - \frac{y}{x}

y^{^{'}} + 5 y = 4

\int \frac{2 x + 1}{x ^{3} - x ^{2} - x + 1} d x

What is the derivative of y=(x^2+1)/(x^3-1)-5x^2 ?
The derivative of y=(x^2+1)/(x^3-1)-5x^2 is (-10x^7+19x^4-3x^2-12x)/((x^3-1)^2)
What is the first derivative of y=(x^2+1)/(x^3-1)-5x^2 ?
The first derivative of y=(x^2+1)/(x^3-1)-5x^2 is (-10x^7+19x^4-3x^2-12x)/((x^3-1)^2)