What is the derivative of (x^3-3x^2+9/(x^2)) ?

The derivative of (x^3-3x^2+9/(x^2)) is (x^3-18)/(x^3)

What is the first derivative of (x^3-3x^2+9/(x^2)) ?

The first derivative of (x^3-3x^2+9/(x^2)) is (x^3-18)/(x^3)

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\frac{d}{d x} (\frac{x ^{3} - 3 x ^{2} + 9}{x ^{2}})

\frac{x ^{3} - 18}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{3} - 3 x ^{2} + 9}{x ^{2}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x ^{3} - 3 x ^{2} + 9 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{3} - 3 x ^{2} + 9 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{3} - 3 x^{2} + 9) = 3 x^{2} - 6 x

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

= \frac{( 3 x ^{2} - 6 x ) x ^{2} - 2 x ( x ^{3} - 3 x ^{2} + 9 )}{( x ^{2} ) ^{2}}

Simplify

\frac{( 3 x ^{2} - 6 x ) x ^{2} - 2 x ( x ^{3} - 3 x ^{2} + 9 )}{( x ^{2} ) ^{2}} : \frac{x ^{3} - 18}{x ^{3}}

= \frac{x ^{3} - 18}{x ^{3}}

\int (x - 2)^{5} d x

\frac{d}{d x} (12 x^{5} + 45 x^{4} - 200 x^{3} + 4)

y = x^{2} - 2, y = x

(9 + x)^{2} (\frac{100}{x ^{2}} + 1)

What is the derivative of (x^3-3x^2+9/(x^2)) ?
The derivative of (x^3-3x^2+9/(x^2)) is (x^3-18)/(x^3)
What is the first derivative of (x^3-3x^2+9/(x^2)) ?
The first derivative of (x^3-3x^2+9/(x^2)) is (x^3-18)/(x^3)