What is the d/(dt)(t*sin(t)) ?

The d/(dt)(t*sin(t)) is sin(t)+tcos(t)

What is the first d/(dt)(t*sin(t)) ?

The first d/(dt)(t*sin(t)) is sin(t)+tcos(t)

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\frac{d}{d t} (t \cdot sin (t))

sin (t) + t cos (t)

Solution steps

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

Apply the Product Rule:

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

f = t, g = sin (t)

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

\frac{d t}{d t} = 1

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

= 1 \cdot sin (t) + cos (t) t

Simplify

= sin (t) + t cos (t)

x y^{2} y^{^{'}} = x + 4

\frac{d}{d x} (3 cot (\frac{x}{8}))

\int z e^{2 z} d z

y^{^{''}} = 6 t^{2}

\int_{0}^{6} x^{3} x^{2} + 36 d x

What is the d/(dt)(t*sin(t)) ?
The d/(dt)(t*sin(t)) is sin(t)+tcos(t)
What is the first d/(dt)(t*sin(t)) ?
The first d/(dt)(t*sin(t)) is sin(t)+tcos(t)