What is the derivative of (a+bx+cx^2/x) ?

The derivative of (a+bx+cx^2/x) is (cx^2-a)/(x^2)

What is the first derivative of (a+bx+cx^2/x) ?

The first derivative of (a+bx+cx^2/x) is (cx^2-a)/(x^2)

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\frac{d}{d x} (\frac{a + b x + c x ^{2}}{x})

\frac{c x ^{2} - a}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{a + b x + c x ^{2}}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( a + b x + c x ^{2} ) x - \frac{d x}{d x} ( a + b x + c x ^{2} )}{x ^{2}}

\frac{d}{d x} (a + b x + c x^{2}) = 2 c x + b

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

= \frac{( 2 c x + b ) x - 1 \cdot ( a + b x + c x ^{2} )}{x ^{2}}

Simplify

\frac{( 2 c x + b ) x - 1 \cdot ( a + b x + c x ^{2} )}{x ^{2}} : \frac{c x ^{2} - a}{x ^{2}}

= \frac{c x ^{2} - a}{x ^{2}}

f (x) = x - 1, (17, 4)

n = 0 \sum \infty 4 - sin (n)

\int_{0}^{2} \frac{1}{e ^{π x}} d x

\frac{d y}{d x} + 4 y = e^{- 4 x}

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

What is the derivative of (a+bx+cx^2/x) ?
The derivative of (a+bx+cx^2/x) is (cx^2-a)/(x^2)
What is the first derivative of (a+bx+cx^2/x) ?
The first derivative of (a+bx+cx^2/x) is (cx^2-a)/(x^2)