What is the derivative of 3cos^3(t) ?

The derivative of 3cos^3(t) is -9cos^2(t)sin(t)

What is the first derivative of 3cos^3(t) ?

The first derivative of 3cos^3(t) is -9cos^2(t)sin(t)

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derivative of

3 cos^{3} (t)

- 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)

What is the derivative of 3cos^3(t) ?
The derivative of 3cos^3(t) is -9cos^2(t)sin(t)
What is the first derivative of 3cos^3(t) ?
The first derivative of 3cos^3(t) is -9cos^2(t)sin(t)