What is (\partial)/(\partial t)(tsin(t)) ?

The answer to (\partial)/(\partial t)(tsin(t)) is sin(t)+tcos(t)

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(\partial)/(\partial t)(tsin(t))

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

sin (t) + t cos (t)

Solution steps

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

Apply the Product Rule:

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

f = t, g = sin (t)

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

\frac{\partial}{\partial t} (t) = 1

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

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

Simplify

= sin (t) + t cos (t)

\frac{d}{d x} (arcsin (x + 1))

\int_{2}^{x^{2}} cos (x^{2} + 1) d x

\int_{0}^{2 π} x^{2} sin (2 x) d x

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

(\frac{2 y}{x} + 2 x) + (2 ln (x) - 3) y^{^{'}} = 0

What is (\partial)/(\partial t)(tsin(t)) ?
The answer to (\partial)/(\partial t)(tsin(t)) is sin(t)+tcos(t)