What is the d/(dt)(12t^2sin(t)) ?

The d/(dt)(12t^2sin(t)) is 12(2tsin(t)+cos(t)t^2)

What is the first d/(dt)(12t^2sin(t)) ?

The first d/(dt)(12t^2sin(t)) is 12(2tsin(t)+cos(t)t^2)

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\frac{d}{d t} (12 t^{2} sin (t))

12 (2 t sin (t) + cos (t) t^{2})

Solution steps

\frac{d}{d t} (12 t^{2} sin (t))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 12 \frac{d}{d t} (t^{2} sin (t))

Apply the Product Rule:

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

f = t^{2}, g = sin (t)

= 12 (\frac{d}{d t} (t^{2}) sin (t) + \frac{d}{d t} (sin (t)) t^{2})

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

\frac{d}{d t} (sin (t)) = cos (t)

= 12 (2 t sin (t) + cos (t) t^{2})

What is the d/(dt)(12t^2sin(t)) ?
The d/(dt)(12t^2sin(t)) is 12(2tsin(t)+cos(t)t^2)
What is the first d/(dt)(12t^2sin(t)) ?
The first d/(dt)(12t^2sin(t)) is 12(2tsin(t)+cos(t)t^2)