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

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

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

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

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

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

Solution steps

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

Take the constant out:

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

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

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

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

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

Simplify

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

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

y^{^{'}} = 0.1 ln (\frac{4000}{y}) y, y (0) = 500

\frac{d}{d x} (6 π x^{2})

\frac{d}{d x} (e^{\frac{x}{5}})

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

\int_{1}^{t} 35 x^{- 3} d x

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