What is the derivative of (-3x^6-x^5+3x^4)/(x^2) ?

The derivative of (-3x^6-x^5+3x^4)/(x^2) is -12x^3-3x^2+6x

What is the first derivative of (-3x^6-x^5+3x^4)/(x^2) ?

The first derivative of (-3x^6-x^5+3x^4)/(x^2) is -12x^3-3x^2+6x

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derivative of

\frac{- 3 x ^{6} - x ^{5} + 3 x ^{4}}{x ^{2}}

- 12 x^{3} - 3 x^{2} + 6 x

Solution steps

\frac{d}{d x} (\frac{- 3 x ^{6} - x ^{5} + 3 x ^{4}}{x ^{2}})

Simplify

\frac{- 3 x ^{6} - x ^{5} + 3 x ^{4}}{x ^{2}} : x^{2} (- 3 x^{2} - x + 3)

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = - 3 x^{2} - x + 3

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

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

\frac{d}{d x} (- 3 x^{2} - x + 3) = - 6 x - 1

= 2 x (- 3 x^{2} - x + 3) + (- 6 x - 1) x^{2}

Simplify

2 x (- 3 x^{2} - x + 3) + (- 6 x - 1) x^{2} : - 12 x^{3} - 3 x^{2} + 6 x

= - 12 x^{3} - 3 x^{2} + 6 x

n = 1 \sum \infty (- \frac{1}{2})^{n - 1}

\frac{d}{d x} (- \frac{5}{2} x^{9})

\int_{0}^{x} ln (x) d x

\frac{d ^{2}}{d x ^{2}} (x^{3} + 3 x^{2} - 2 x + 8)

\frac{d y}{d x} = \frac{x}{y}, y (1) = 2

What is the derivative of (-3x^6-x^5+3x^4)/(x^2) ?
The derivative of (-3x^6-x^5+3x^4)/(x^2) is -12x^3-3x^2+6x
What is the first derivative of (-3x^6-x^5+3x^4)/(x^2) ?
The first derivative of (-3x^6-x^5+3x^4)/(x^2) is -12x^3-3x^2+6x