What is the derivative of x/(2.4(c^2+cx)(c^2-x^2)) ?

The derivative of x/(2.4(c^2+cx)(c^2-x^2)) is (0.41666…c(-2x^3-3cx^2+c^3))/((c^2+cx)^2)

What is the first derivative of x/(2.4(c^2+cx)(c^2-x^2)) ?

The first derivative of x/(2.4(c^2+cx)(c^2-x^2)) is (0.41666…c(-2x^3-3cx^2+c^3))/((c^2+cx)^2)

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\frac{d}{d x} (\frac{x}{2.4 ( c ^{2} + c x )} (c^{2} - x^{2}))

\frac{0.41666 \dots c ( - 2 x ^{3} - 3 c x ^{2} + c ^{3} )}{( c ^{2} + c x ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{2.4 ( c ^{2} + c x )} (c^{2} - x^{2}))

Take the constant out:

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

= \frac{1}{2.4} \frac{d}{d x} (\frac{x}{c ^{2} + c x} (c^{2} - x^{2}))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{x}{c ^{2} + c x}, g = c^{2} - x^{2}

= \frac{1}{2.4} (\frac{d}{d x} (\frac{x}{c ^{2} + c x}) (c^{2} - x^{2}) + \frac{d}{d x} (c^{2} - x^{2}) \frac{x}{c ^{2} + c x})

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

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

= \frac{1}{2.4} (\frac{c ^{2}}{( c ^{2} + c x ) ^{2}} (c^{2} - x^{2}) + (- 2 x) \frac{x}{c ^{2} + c x})

Simplify

\frac{1}{2.4} (\frac{c ^{2}}{( c ^{2} + c x ) ^{2}} (c^{2} - x^{2}) + (- 2 x) \frac{x}{c ^{2} + c x}) : \frac{0.41666 \dots c ( - 2 x ^{3} - 3 c x ^{2} + c ^{3} )}{( c ^{2} + c x ) ^{2}}

= \frac{0.41666 \dots c ( - 2 x ^{3} - 3 c x ^{2} + c ^{3} )}{( c ^{2} + c x ) ^{2}}

\int \frac{cos ( 2 t )}{( 1 + sin ( 2 t ) ) ^{4}} d t

x \to - 1 lim (\frac{x + 2}{x ^{3} + 1})

\int x x (1 + x^{2} x)^{4} d x

y^{3} - (6 x + 6) + 3 x y^{2} y^{^{'}} = 0

\frac{d y}{d x} = \frac{x ^{2}}{y ^{2}}

What is the derivative of x/(2.4(c^2+cx)(c^2-x^2)) ?
The derivative of x/(2.4(c^2+cx)(c^2-x^2)) is (0.41666…c(-2x^3-3cx^2+c^3))/((c^2+cx)^2)
What is the first derivative of x/(2.4(c^2+cx)(c^2-x^2)) ?
The first derivative of x/(2.4(c^2+cx)(c^2-x^2)) is (0.41666…c(-2x^3-3cx^2+c^3))/((c^2+cx)^2)