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Popular >

derivative of 2t^3cos(t)

Solution

derivative of

2 t^{3} cos (t)

Solution

2 (3 t^{2} cos (t) - t^{3} sin (t))

Solution steps

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

Take the constant out:

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

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

Apply the Product Rule:

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

f = t^{3}, g = cos (t)

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

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

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

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

Simplify

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

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Frequently Asked Questions (FAQ)

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