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

The derivative of ((5x-25))/(x^2-5x) is -5/(x^2)

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

The first derivative of ((5x-25))/(x^2-5x) is -5/(x^2)

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derivative of

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

- \frac{5}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

\frac{d}{d x} (5 x - 25) = 5

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

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

Simplify

\frac{5 ( x ^{2} - 5 x ) - ( 2 x - 5 ) ( 5 x - 25 )}{( x ^{2} - 5 x ) ^{2}} : - \frac{5}{x ^{2}}

= - \frac{5}{x ^{2}}

y^{^{''}} + 4 y = - 12 sec (2 t)

y = 4 - 2 x - x^{- 3}

x \to - 2 lim (\frac{x - 2}{x + 2})

y^{^{'}} = \frac{x e ^{x^{2}}}{2}

\frac{\partial}{\partial x} (2 x^{0.3} y^{0.3})

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