What is the derivative of (x^3-5x^2+1)/(x^2) ?

The derivative of (x^3-5x^2+1)/(x^2) is (x^3-2)/(x^3)

What is the first derivative of (x^3-5x^2+1)/(x^2) ?

The first derivative of (x^3-5x^2+1)/(x^2) is (x^3-2)/(x^3)

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derivative of

\frac{x ^{3} - 5 x ^{2} + 1}{x ^{2}}

\frac{x ^{3} - 2}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{3} - 5 x ^{2} + 1}{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} - 5 x ^{2} + 1 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{3} - 5 x ^{2} + 1 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{3} - 5 x^{2} + 1) = 3 x^{2} - 10 x

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

= \frac{( 3 x ^{2} - 10 x ) x ^{2} - 2 x ( x ^{3} - 5 x ^{2} + 1 )}{( x ^{2} ) ^{2}}

Simplify

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

= \frac{x ^{3} - 2}{x ^{3}}

\int_{0}^{\frac{1}{2}} 5 arcsin (2 y) d y

\int \frac{1}{x ^{2} x ^{2} - 100} d x

f (x) = \frac{sec ( x )}{8 + sec ( x )}

\int \frac{1}{x ^{3} x ^{2} - 100} d x

\frac{d}{d x} (3 x^{3} e^{- x})

What is the derivative of (x^3-5x^2+1)/(x^2) ?
The derivative of (x^3-5x^2+1)/(x^2) is (x^3-2)/(x^3)
What is the first derivative of (x^3-5x^2+1)/(x^2) ?
The first derivative of (x^3-5x^2+1)/(x^2) is (x^3-2)/(x^3)