What is the d/(dt)(4cos^3(t)) ?

The d/(dt)(4cos^3(t)) is -12cos^2(t)sin(t)

What is the first d/(dt)(4cos^3(t)) ?

The first d/(dt)(4cos^3(t)) is -12cos^2(t)sin(t)

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\frac{d}{d t} (4 cos^{3} (t))

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

Solution steps

\frac{d}{d t} (4 cos^{3} (t))

Take the constant out:

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

= 4 \frac{d}{d t} (cos^{3} (t))

Apply the chain rule:

3 (cos (t))^{2} \frac{d}{d t} (cos (t))

= 3 (cos (t))^{2} \frac{d}{d t} (cos (t))

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

= 4 \cdot 3 (cos (t))^{2} (- sin (t))

Simplify

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

What is the d/(dt)(4cos^3(t)) ?
The d/(dt)(4cos^3(t)) is -12cos^2(t)sin(t)
What is the first d/(dt)(4cos^3(t)) ?
The first d/(dt)(4cos^3(t)) is -12cos^2(t)sin(t)