What is the derivative of ((x-3(3x-25))/x) ?

The derivative of ((x-3(3x-25))/x) is (3x^2-75)/(x^2)

What is the first derivative of ((x-3(3x-25))/x) ?

The first derivative of ((x-3(3x-25))/x) is (3x^2-75)/(x^2)

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\frac{d}{d x} (\frac{( x - 3 ) ( 3 x - 25 )}{x})

\frac{3 x ^{2} - 75}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{( x - 3 ) ( 3 x - 25 )}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((x - 3) (3 x - 25)) = 6 x - 34

\frac{d x}{d x} = 1

= \frac{( 6 x - 34 ) x - 1 \cdot ( x - 3 ) ( 3 x - 25 )}{x ^{2}}

Simplify

\frac{( 6 x - 34 ) x - 1 \cdot ( x - 3 ) ( 3 x - 25 )}{x ^{2}} : \frac{3 x ^{2} - 75}{x ^{2}}

= \frac{3 x ^{2} - 75}{x ^{2}}

f (x) = x^{2} + 5 x - 2, at x = - 1

x \to 0 + lim (\frac{6}{x ^{2} - x})

f (x) = x - 5

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

\frac{\partial}{\partial x} ((2 x + 8 y)^{3})

What is the derivative of ((x-3(3x-25))/x) ?
The derivative of ((x-3(3x-25))/x) is (3x^2-75)/(x^2)
What is the first derivative of ((x-3(3x-25))/x) ?
The first derivative of ((x-3(3x-25))/x) is (3x^2-75)/(x^2)