What is the d/(dt)((x)(t^3-2)) ?

The d/(dt)((x)(t^3-2)) is (dx)/(dt)(t^3-2)+3t^2x

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

The first d/(dt)((x)(t^3-2)) is (dx)/(dt)(t^3-2)+3t^2x

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

- \frac{1}{2} (x - 2)^{2}

\frac{d}{d t} ((x) (t + t))

(- a - x) (a + x)

(2 e^{2 t} + 2)^{2}

(e^{y} - y e^{y}) d y

What is the d/(dt)((x)(t^3-2)) ?
The d/(dt)((x)(t^3-2)) is (dx)/(dt)(t^3-2)+3t^2x
What is the first d/(dt)((x)(t^3-2)) ?
The first d/(dt)((x)(t^3-2)) is (dx)/(dt)(t^3-2)+3t^2x