What is (\partial)/(\partial t)(-te^tsin(x)) ?

The answer to (\partial)/(\partial t)(-te^tsin(x)) is -sin(x)(e^t+e^tt)

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(\partial)/(\partial t)(-te^tsin(x))

\frac{\partial}{\partial t} (- t e^{t} sin (x))

- sin (x) (e^{t} + e^{t} t)

Solution steps

\frac{\partial}{\partial t} (- t e^{t} sin (x))

Treat

x

as a constant

Take the constant out:

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

= - sin (x) \frac{\partial}{\partial t} (t e^{t})

Apply the Product Rule:

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

f = t, g = e^{t}

= - sin (x) (\frac{\partial}{\partial t} (t) e^{t} + \frac{\partial}{\partial t} (e^{t}) t)

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

\frac{\partial}{\partial t} (e^{t}) = e^{t}

= - sin (x) (1 \cdot e^{t} + e^{t} t)

Simplify

= - sin (x) (e^{t} + e^{t} t)

\int_{0}^{5} ∣ 2 x - 5 ∣ d x

\frac{d}{d x} (2 x + 6)

y = x (x^{2} + 7)^{4}

\frac{\partial}{\partial x} (4 e^{x y})

y = x, y = 4, x = 0, x = 22

What is (\partial)/(\partial t)(-te^tsin(x)) ?
The answer to (\partial)/(\partial t)(-te^tsin(x)) is -sin(x)(e^t+e^tt)