What is the d/(dt)(t^2sin(wt)) ?

The d/(dt)(t^2sin(wt)) is 2tsin(wt)+cos(wt)wt^2

What is the first d/(dt)(t^2sin(wt)) ?

The first d/(dt)(t^2sin(wt)) is 2tsin(wt)+cos(wt)wt^2

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\frac{d}{d t} (t^{2} sin (wt))

2 t sin (wt) + cos (wt) w t^{2}

Solution steps

\frac{d}{d t} (t^{2} sin (wt))

Treat

w

as a constant

Apply the Product Rule:

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

f = t^{2}, g = sin (wt)

= \frac{d}{d t} (t^{2}) sin (wt) + \frac{d}{d t} (sin (wt)) t^{2}

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

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

= 2 t sin (wt) + cos (wt) w t^{2}

t a y l or e^{5 x}

t a y l or \frac{1}{( 1 - 3 x ^{2} )}, x = 0.577

d er i v a t i v e (2 x^{3} + 2) (x^{4} - 3 x)

\int \frac{u + 1}{u ^{2} + 1} d u

d er i v a t i v e f (x) = \frac{e ^{x}}{1 + e ^{x}}

What is the d/(dt)(t^2sin(wt)) ?
The d/(dt)(t^2sin(wt)) is 2tsin(wt)+cos(wt)wt^2
What is the first d/(dt)(t^2sin(wt)) ?
The first d/(dt)(t^2sin(wt)) is 2tsin(wt)+cos(wt)wt^2