What is the derivative of (t^2-4t)(t^2+4t) ?

The derivative of (t^2-4t)(t^2+4t) is 4t^3-32t

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

The first derivative of (t^2-4t)(t^2+4t) is 4t^3-32t

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derivative of

(t^{2} - 4 t) (t^{2} + 4 t)

4 t^{3} - 32 t

Solution steps

\frac{d}{d t} ((t^{2} - 4 t) (t^{2} + 4 t))

Apply the Product Rule:

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

f = t^{2} - 4 t, g = t^{2} + 4 t

= \frac{d}{d t} (t^{2} - 4 t) (t^{2} + 4 t) + \frac{d}{d t} (t^{2} + 4 t) (t^{2} - 4 t)

\frac{d}{d t} (t^{2} - 4 t) = 2 t - 4

\frac{d}{d t} (t^{2} + 4 t) = 2 t + 4

= (2 t - 4) (t^{2} + 4 t) + (2 t + 4) (t^{2} - 4 t)

Simplify

(2 t - 4) (t^{2} + 4 t) + (2 t + 4) (t^{2} - 4 t) : 4 t^{3} - 32 t

= 4 t^{3} - 32 t

What is the derivative of (t^2-4t)(t^2+4t) ?
The derivative of (t^2-4t)(t^2+4t) is 4t^3-32t
What is the first derivative of (t^2-4t)(t^2+4t) ?
The first derivative of (t^2-4t)(t^2+4t) is 4t^3-32t