What is the derivative of (24x(x^2+1)/((1-x^2)^4)) ?

The derivative of (24x(x^2+1)/((1-x^2)^4)) is (24(5x^4+10x^2+1))/((1-x^2)^5)

What is the first derivative of (24x(x^2+1)/((1-x^2)^4)) ?

The first derivative of (24x(x^2+1)/((1-x^2)^4)) is (24(5x^4+10x^2+1))/((1-x^2)^5)

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\frac{d}{d x} (\frac{24 x ( x ^{2} + 1 )}{( 1 - x ^{2} ) ^{4}})

\frac{24 ( 5 x ^{4} + 10 x ^{2} + 1 )}{( 1 - x ^{2} ) ^{5}}

Solution steps

\frac{d}{d x} (\frac{24 x ( x ^{2} + 1 )}{( 1 - x ^{2} ) ^{4}})

Take the constant out:

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

= 24 \frac{d}{d x} (\frac{x ( x ^{2} + 1 )}{( 1 - x ^{2} ) ^{4}})

Apply the Quotient Rule:

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

= 24 \cdot \frac{\frac{d}{d x} ( x ( x ^{2} + 1 ) ) ( 1 - x ^{2} ) ^{4} - \frac{d}{d x} ( ( 1 - x ^{2} ) ^{4} ) x ( x ^{2} + 1 )}{( ( 1 - x ^{2} ) ^{4} ) ^{2}}

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

\frac{d}{d x} ((1 - x^{2})^{4}) = - 8 x (1 - x^{2})^{3}

= 24 \cdot \frac{( 3 x ^{2} + 1 ) ( 1 - x ^{2} ) ^{4} - ( - 8 x ( 1 - x ^{2} ) ^{3} ) x ( x ^{2} + 1 )}{( ( 1 - x ^{2} ) ^{4} ) ^{2}}

Simplify

24 \cdot \frac{( 3 x ^{2} + 1 ) ( 1 - x ^{2} ) ^{4} - ( - 8 x ( 1 - x ^{2} ) ^{3} ) x ( x ^{2} + 1 )}{( ( 1 - x ^{2} ) ^{4} ) ^{2}} : \frac{24 ( 5 x ^{4} + 10 x ^{2} + 1 )}{( 1 - x ^{2} ) ^{5}}

= \frac{24 ( 5 x ^{4} + 10 x ^{2} + 1 )}{( 1 - x ^{2} ) ^{5}}

\int \frac{x ^{2} ln ( x )}{2} d x

n = 0 \sum \infty \frac{n ^{2}}{e ^{n}}

\int_{0}^{π} (cos (x))^{6} d x

\int_{2}^{4} 2 cos (π x) d x

\int 16 - 7 x^{2} d x

What is the derivative of (24x(x^2+1)/((1-x^2)^4)) ?
The derivative of (24x(x^2+1)/((1-x^2)^4)) is (24(5x^4+10x^2+1))/((1-x^2)^5)
What is the first derivative of (24x(x^2+1)/((1-x^2)^4)) ?
The first derivative of (24x(x^2+1)/((1-x^2)^4)) is (24(5x^4+10x^2+1))/((1-x^2)^5)