What is the derivative of f(x)=(x^3-8x^2+5)/(x^2) ?

The derivative of f(x)=(x^3-8x^2+5)/(x^2) is (x^3-10)/(x^3)

What is the first derivative of f(x)=(x^3-8x^2+5)/(x^2) ?

The first derivative of f(x)=(x^3-8x^2+5)/(x^2) is (x^3-10)/(x^3)

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derivative of

f (x) = \frac{x ^{3} - 8 x ^{2} + 5}{x ^{2}}

\frac{x ^{3} - 10}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{x ^{3} - 8 x ^{2} + 5}{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} - 8 x ^{2} + 5 ) x ^{2} - \frac{d}{d x} ( x ^{2} ) ( x ^{3} - 8 x ^{2} + 5 )}{( x ^{2} ) ^{2}}

\frac{d}{d x} (x^{3} - 8 x^{2} + 5) = 3 x^{2} - 16 x

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

= \frac{( 3 x ^{2} - 16 x ) x ^{2} - 2 x ( x ^{3} - 8 x ^{2} + 5 )}{( x ^{2} ) ^{2}}

Simplify

\frac{( 3 x ^{2} - 16 x ) x ^{2} - 2 x ( x ^{3} - 8 x ^{2} + 5 )}{( x ^{2} ) ^{2}} : \frac{x ^{3} - 10}{x ^{3}}

= \frac{x ^{3} - 10}{x ^{3}}

3 e^{y}

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

\frac{d}{d x} (- 2 x^{2} + \frac{5}{3} x + 11)

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

\frac{d}{d x} (- 5 x^{\frac{4}{5}} + 3 x^{\frac{2}{3}} + 2)

What is the derivative of f(x)=(x^3-8x^2+5)/(x^2) ?
The derivative of f(x)=(x^3-8x^2+5)/(x^2) is (x^3-10)/(x^3)
What is the first derivative of f(x)=(x^3-8x^2+5)/(x^2) ?
The first derivative of f(x)=(x^3-8x^2+5)/(x^2) is (x^3-10)/(x^3)