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Popular Calculus >

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

Solution

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

Solution

\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}}

Graph

Popular Examples

(dy)/(dx)+4y=e^{-4x}

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

(\partial)/(\partial x)(3x^2-3)

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

integral of (x-1)/(x^2(x+1)^2)

\int \frac{x - 1}{x ^{2} ( x + 1 ) ^{2}} d x

tangent of f(x)= 7/(x^2)-6x^2,\at x=5

t an g e n t f (x) = \frac{7}{x ^{2}} - 6 x^{2}, at x = 5

derivative of sqrt(2x^2+1)

\frac{d}{d x} (2 x^{2} + 1)

Frequently Asked Questions (FAQ)

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)