What is the derivative of (40+24x^4/(1+4x^4)) ?

The derivative of (40+24x^4/(1+4x^4)) is -(544x^3)/((1+4x^4)^2)

What is the first derivative of (40+24x^4/(1+4x^4)) ?

The first derivative of (40+24x^4/(1+4x^4)) is -(544x^3)/((1+4x^4)^2)

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\frac{d}{d x} (\frac{40 + 24 x ^{4}}{1 + 4 x ^{4}})

- \frac{544 x ^{3}}{( 1 + 4 x ^{4} ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{40 + 24 x ^{4}}{1 + 4 x ^{4}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 40 + 24 x ^{4} ) ( 1 + 4 x ^{4} ) - \frac{d}{d x} ( 1 + 4 x ^{4} ) ( 40 + 24 x ^{4} )}{( 1 + 4 x ^{4} ) ^{2}}

\frac{d}{d x} (40 + 24 x^{4}) = 96 x^{3}

\frac{d}{d x} (1 + 4 x^{4}) = 16 x^{3}

= \frac{96 x ^{3} ( 1 + 4 x ^{4} ) - 16 x ^{3} ( 40 + 24 x ^{4} )}{( 1 + 4 x ^{4} ) ^{2}}

Simplify

\frac{96 x ^{3} ( 1 + 4 x ^{4} ) - 16 x ^{3} ( 40 + 24 x ^{4} )}{( 1 + 4 x ^{4} ) ^{2}} : - \frac{544 x ^{3}}{( 1 + 4 x ^{4} ) ^{2}}

= - \frac{544 x ^{3}}{( 1 + 4 x ^{4} ) ^{2}}

\frac{x}{x + 6}

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

x \to 0 lim (\frac{5 x ^{2}}{x ^{2}})

\int_{- 1}^{1} π (1 - x^{2})^{2} d x

f (t) = (4 t^{2} + 5)

What is the derivative of (40+24x^4/(1+4x^4)) ?
The derivative of (40+24x^4/(1+4x^4)) is -(544x^3)/((1+4x^4)^2)
What is the first derivative of (40+24x^4/(1+4x^4)) ?
The first derivative of (40+24x^4/(1+4x^4)) is -(544x^3)/((1+4x^4)^2)