What is (\partial)/(\partial x)(4xye^x) ?

The answer to (\partial)/(\partial x)(4xye^x) is 4y(e^x+e^xx)

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(\partial)/(\partial x)(4xye^x)

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

4 y (e^{x} + e^{x} x)

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = x, g = e^{x}

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

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

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

= 4 y (1 \cdot e^{x} + e^{x} x)

Simplify

= 4 y (e^{x} + e^{x} x)

x \to 2 lim (3 x^{4} + 2 x^{2} - x + 1)

x \to - 8 lim (x^{3})

y^{^{''}} + 25 y = e^{- t}

k = 1 \sum \infty \frac{1}{k ( k + 1 )}

\int 0.02 e^{- 0.02 x} d x

What is (\partial)/(\partial x)(4xye^x) ?
The answer to (\partial)/(\partial x)(4xye^x) is 4y(e^x+e^xx)