What is the d/(dt)((x)(-5x^2(x-2))) ?

The d/(dt)((x)(-5x^2(x-2))) is -5(4t^3-6t^2)

What is the first d/(dt)((x)(-5x^2(x-2))) ?

The first d/(dt)((x)(-5x^2(x-2))) is -5(4t^3-6t^2)

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\frac{d}{d t} ((t) (- 5 t^{2} (t - 2)))

- 5 (4 t^{3} - 6 t^{2})

Solution steps

\frac{d}{d t} ((t) (- 5 t^{2} (t - 2)))

Simplify

(t) (- 5 t^{2} (t - 2)) : - 5 t^{3} (t - 2)

= \frac{d}{d t} (- 5 t^{3} (t - 2))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= - 5 \frac{d}{d t} (t^{3} (t - 2))

Apply the Product Rule:

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

f = t^{3}, g = t - 2

= - 5 (\frac{d}{d t} (t^{3}) (t - 2) + \frac{d}{d t} (t - 2) t^{3})

\frac{d}{d t} (t^{3}) = 3 t^{2}

\frac{d}{d t} (t - 2) = 1

= - 5 (3 t^{2} (t - 2) + 1 \cdot t^{3})

Simplify

- 5 (3 t^{2} (t - 2) + 1 \cdot t^{3}) : - 5 (4 t^{3} - 6 t^{2})

= - 5 (4 t^{3} - 6 t^{2})

\frac{3 x + 11}{( x + 3 ) ( 3 x + 1 )}

(x - 3 x)^{2}

(t sin (t^{2})) (sin (t^{2}) + 2 t^{2} cos (t^{2}))

x (x^{2} + y^{2}) x^{2} + y^{2}

50 ln (- 5) + 50 - \frac{25 ( 12 ln ( - 5 ) + 11 )}{6}

What is the d/(dt)((x)(-5x^2(x-2))) ?
The d/(dt)((x)(-5x^2(x-2))) is -5(4t^3-6t^2)
What is the first d/(dt)((x)(-5x^2(x-2))) ?
The first d/(dt)((x)(-5x^2(x-2))) is -5(4t^3-6t^2)