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

The d/(dt)(-12cos^2(t)sin(t)) is -12(-2cos(t)+3cos^3(t))

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

The first d/(dt)(-12cos^2(t)sin(t)) is -12(-2cos(t)+3cos^3(t))

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

- 12 (- 2 cos (t) + 3 cos^{3} (t))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

- 12 ((- sin (2 t)) sin (t) + cos (t) cos^{2} (t)) : - 12 (- 2 cos (t) + 3 cos^{3} (t))

= - 12 (- 2 cos (t) + 3 cos^{3} (t))

What is the d/(dt)(-12cos^2(t)sin(t)) ?
The d/(dt)(-12cos^2(t)sin(t)) is -12(-2cos(t)+3cos^3(t))
What is the first d/(dt)(-12cos^2(t)sin(t)) ?
The first d/(dt)(-12cos^2(t)sin(t)) is -12(-2cos(t)+3cos^3(t))