What is the derivative of ((x+2(x^2-2x+4))/(x^3)) ?

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

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

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

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

- \frac{24}{x ^{4}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

\frac{3 x ^{2} x ^{3} - 3 x ^{2} ( x + 2 ) ( x ^{2} - 2 x + 4 )}{( x ^{3} ) ^{2}} : - \frac{24}{x ^{4}}

= - \frac{24}{x ^{4}}

\int \frac{1}{x ^{2} x ^{2} - 169} d x

\int \frac{1 - x ^{2}}{x ^{2}} d x

y^{^{''}} + 4 y^{^{'}} + 20 y = 80

y = x, y = x - 2, y = 0

\int \frac{1}{( x ^{2} + 81 ) ^{2}} d x

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