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Popular >

d/(dt)((x)(t^3-t^2))

Solution

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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Frequently Asked Questions (FAQ)

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