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Popular >

d/(dt)((x)(12-3t^3))

Solution

\frac{d}{d t} ((x) (12 - 3 t^{3}))

Solution

\frac{d x}{d t} (12 - 3 t^{3}) - 9 t^{2} x

Solution steps

\frac{d}{d t} ((x) (12 - 3 t^{3}))

Apply the Product Rule:

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

f = x, g = 12 - 3 t^{3}

= \frac{d x}{d t} (12 - 3 t^{3}) + \frac{d}{d t} (12 - 3 t^{3}) x

\frac{d}{d t} (12 - 3 t^{3}) = - 9 t^{2}

= \frac{d x}{d t} (12 - 3 t^{3}) + (- 9 t^{2}) x

Simplify

= \frac{d x}{d t} (12 - 3 t^{3}) - 9 t^{2} x

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Frequently Asked Questions (FAQ)

What is the d/(dt)((x)(12-3t^3)) ?
The d/(dt)((x)(12-3t^3)) is (dx)/(dt)(12-3t^3)-9t^2x
What is the first d/(dt)((x)(12-3t^3)) ?
The first d/(dt)((x)(12-3t^3)) is (dx)/(dt)(12-3t^3)-9t^2x