What is the derivative of ((x+5(x^2-5x+25))/(x^3)) ?

The derivative of ((x+5(x^2-5x+25))/(x^3)) is -(375)/(x^4)

What is the first derivative of ((x+5(x^2-5x+25))/(x^3)) ?

The first derivative of ((x+5(x^2-5x+25))/(x^3)) is -(375)/(x^4)

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\frac{d}{d x} (\frac{( x + 5 ) ( x ^{2} - 5 x + 25 )}{x ^{3}})

- \frac{375}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{( x + 5 ) ( x ^{2} - 5 x + 25 )}{x ^{3}})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( ( x + 5 ) ( x ^{2} - 5 x + 25 ) ) x ^{3} - \frac{d}{d x} ( x ^{3} ) ( x + 5 ) ( x ^{2} - 5 x + 25 )}{( x ^{3} ) ^{2}}

\frac{d}{d x} ((x + 5) (x^{2} - 5 x + 25)) = 3 x^{2}

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

= \frac{3 x ^{2} x ^{3} - 3 x ^{2} ( x + 5 ) ( x ^{2} - 5 x + 25 )}{( x ^{3} ) ^{2}}

Simplify

\frac{3 x ^{2} x ^{3} - 3 x ^{2} ( x + 5 ) ( x ^{2} - 5 x + 25 )}{( x ^{3} ) ^{2}} : - \frac{375}{x ^{4}}

= - \frac{375}{x ^{4}}

\int x^{2} x^{3} + 1 d x

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

f (x) = 2000 (x^{2} + 5)^{\frac{1}{3}}

\int_{0}^{2} e^{- x^{2}} d x

\frac{\partial}{\partial x} (x^{0.5} + y)

What is the derivative of ((x+5(x^2-5x+25))/(x^3)) ?
The derivative of ((x+5(x^2-5x+25))/(x^3)) is -(375)/(x^4)
What is the first derivative of ((x+5(x^2-5x+25))/(x^3)) ?
The first derivative of ((x+5(x^2-5x+25))/(x^3)) is -(375)/(x^4)