What is the derivative of 2/5 x^5-4x^3+9x^2-6x-2 ?

The derivative of 2/5 x^5-4x^3+9x^2-6x-2 is 2x^4-12x^2+18x-6

What is the first derivative of 2/5 x^5-4x^3+9x^2-6x-2 ?

The first derivative of 2/5 x^5-4x^3+9x^2-6x-2 is 2x^4-12x^2+18x-6

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\frac{d}{d x} (\frac{2}{5} x^{5} - 4 x^{3} + 9 x^{2} - 6 x - 2)

2 x^{4} - 12 x^{2} + 18 x - 6

Solution steps

\frac{d}{d x} (\frac{2}{5} x^{5} - 4 x^{3} + 9 x^{2} - 6 x - 2)

Simplify

\frac{2}{5} x^{5} - 4 x^{3} + 9 x^{2} - 6 x - 2 : \frac{2 x ^{5}}{5} - 4 x^{3} + 9 x^{2} - 6 x - 2

= \frac{d}{d x} (\frac{2 x ^{5}}{5} - 4 x^{3} + 9 x^{2} - 6 x - 2)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{2 x ^{5}}{5}) - \frac{d}{d x} (4 x^{3}) + \frac{d}{d x} (9 x^{2}) - \frac{d}{d x} (6 x) - \frac{d}{d x} (2)

\frac{d}{d x} (\frac{2 x ^{5}}{5}) = 2 x^{4}

\frac{d}{d x} (4 x^{3}) = 12 x^{2}

\frac{d}{d x} (9 x^{2}) = 18 x

\frac{d}{d x} (6 x) = 6

\frac{d}{d x} (2) = 0

= 2 x^{4} - 12 x^{2} + 18 x - 6 - 0

Simplify

= 2 x^{4} - 12 x^{2} + 18 x - 6

x \to 1 + lim (ln (x^{5} - 1))

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

arccos (\frac{x}{2})

y^{^{'}} = \frac{2 x + sec ^{2} ( x )}{2 y}, y (0) = - 3

\frac{\partial}{\partial y} (sin (x y^{2} z^{3}))

What is the derivative of 2/5 x^5-4x^3+9x^2-6x-2 ?
The derivative of 2/5 x^5-4x^3+9x^2-6x-2 is 2x^4-12x^2+18x-6
What is the first derivative of 2/5 x^5-4x^3+9x^2-6x-2 ?
The first derivative of 2/5 x^5-4x^3+9x^2-6x-2 is 2x^4-12x^2+18x-6