What is the derivative of f(x)=(x^3-7x^2+7)/(x^2) ?

The derivative of f(x)=(x^3-7x^2+7)/(x^2) is (x^3-14)/(x^3)

What is the first derivative of f(x)=(x^3-7x^2+7)/(x^2) ?

The first derivative of f(x)=(x^3-7x^2+7)/(x^2) is (x^3-14)/(x^3)

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derivative of

f (x) = \frac{x ^{3} - 7 x ^{2} + 7}{x ^{2}}

\frac{x ^{3} - 14}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{3} - 7 x ^{2} + 7}{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} - 7 x ^{2} + 7 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{3} - 7 x ^{2} + 7 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{3} - 7 x^{2} + 7) = 3 x^{2} - 14 x

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

= \frac{( 3 x ^{2} - 14 x ) x ^{2} - 2 x ( x ^{3} - 7 x ^{2} + 7 )}{( x ^{2} ) ^{2}}

Simplify

\frac{( 3 x ^{2} - 14 x ) x ^{2} - 2 x ( x ^{3} - 7 x ^{2} + 7 )}{( x ^{2} ) ^{2}} : \frac{x ^{3} - 14}{x ^{3}}

= \frac{x ^{3} - 14}{x ^{3}}

\frac{\partial}{\partial x} (y^{6} sin (2 x))

x \to \infty lim (- 3 x)

\frac{d}{d x} (a + \frac{1}{x})

1 - x^{2}, x^{2}

\int_{0}^{1} 4 x^{4} e^{- x} d x

What is the derivative of f(x)=(x^3-7x^2+7)/(x^2) ?
The derivative of f(x)=(x^3-7x^2+7)/(x^2) is (x^3-14)/(x^3)
What is the first derivative of f(x)=(x^3-7x^2+7)/(x^2) ?
The first derivative of f(x)=(x^3-7x^2+7)/(x^2) is (x^3-14)/(x^3)