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Popular >

d/(dt)((x)(x^2+3x-6))

Solution

\frac{d}{d t} ((t) (t^{2} + 3 t - 6))

Solution

3 t^{2} + 6 t - 6

Solution steps

\frac{d}{d t} ((t) (t^{2} + 3 t - 6))

Apply the Product Rule:

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

f = t, g = t^{2} + 3 t - 6

= \frac{d t}{d t} (t^{2} + 3 t - 6) + \frac{d}{d t} (t^{2} + 3 t - 6) t

\frac{d t}{d t} = 1

\frac{d}{d t} (t^{2} + 3 t - 6) = 2 t + 3

= 1 \cdot (t^{2} + 3 t - 6) + (2 t + 3) t

Simplify

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

= 3 t^{2} + 6 t - 6

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Frequently Asked Questions (FAQ)

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