What is (\partial)/(\partial t)(xe^{2t}-4x) ?

The answer to (\partial)/(\partial t)(xe^{2t}-4x) is 2e^{2t}x

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(\partial)/(\partial t)(xe^{2t}-4x)

\frac{\partial}{\partial t} (x e^{2 t} - 4 x)

2 e^{2 t} x

Solution steps

\frac{\partial}{\partial t} (x e^{2 t} - 4 x)

Treat

x

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial t} (x e^{2 t}) - \frac{\partial}{\partial t} (4 x)

\frac{\partial}{\partial t} (x e^{2 t}) = x e^{2 t} \cdot 2

\frac{\partial}{\partial t} (4 x) = 0

= x e^{2 t} \cdot 2 - 0

Simplify

= 2 e^{2 t} x

\int_{- 1}^{2} 2^{x} d x

n = 0 \sum \infty e^{- \frac{n}{2}}

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

\frac{d}{d x} (uv w z (u, v, w, x))

x \to 3 - lim (x - 1)

What is (\partial)/(\partial t)(xe^{2t}-4x) ?
The answer to (\partial)/(\partial t)(xe^{2t}-4x) is 2e^{2t}x