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

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

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

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

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derivative of

t^{3} sin (t)

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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