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Popular >

derivative of (t^2-2t)(t^2+2t)

Solution

derivative of

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

Solution

4 t^{3} - 8 t

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= (2 t - 2) (t^{2} + 2 t) + (2 t + 2) (t^{2} - 2 t)

Simplify

(2 t - 2) (t^{2} + 2 t) + (2 t + 2) (t^{2} - 2 t) : 4 t^{3} - 8 t

= 4 t^{3} - 8 t

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\frac{1}{2}

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Frequently Asked Questions (FAQ)

What is the derivative of (t^2-2t)(t^2+2t) ?
The derivative of (t^2-2t)(t^2+2t) is 4t^3-8t
What is the first derivative of (t^2-2t)(t^2+2t) ?
The first derivative of (t^2-2t)(t^2+2t) is 4t^3-8t