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Popular Calculus >

d/(dt)(3cos^3(t))

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

= 3 \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)

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

Simplify

= - 9 cos^{2} (t) sin (t)

Graph

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Frequently Asked Questions (FAQ)

What is the d/(dt)(3cos^3(t)) ?
The d/(dt)(3cos^3(t)) is -9cos^2(t)sin(t)
What is the first d/(dt)(3cos^3(t)) ?
The first d/(dt)(3cos^3(t)) is -9cos^2(t)sin(t)