What is the derivative of (10x^3/(x^2-1)) ?

The derivative of (10x^3/(x^2-1)) is (10(x^4-3x^2))/((x^2-1)^2)

What is the first derivative of (10x^3/(x^2-1)) ?

The first derivative of (10x^3/(x^2-1)) is (10(x^4-3x^2))/((x^2-1)^2)

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

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

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

\frac{d}{d x} (x^{3}) = 3 x^{2}

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

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

Simplify

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

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

What is the derivative of (10x^3/(x^2-1)) ?
The derivative of (10x^3/(x^2-1)) is (10(x^4-3x^2))/((x^2-1)^2)
What is the first derivative of (10x^3/(x^2-1)) ?
The first derivative of (10x^3/(x^2-1)) is (10(x^4-3x^2))/((x^2-1)^2)