What is (\partial)/(\partial x)((2x+5y)e^y) ?

The answer to (\partial)/(\partial x)((2x+5y)e^y) is 2e^y

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(\partial)/(\partial x)((2x+5y)e^y)

\frac{\partial}{\partial x} ((2 x + 5 y) e^{y})

2 e^{y}

Solution steps

\frac{\partial}{\partial x} ((2 x + 5 y) e^{y})

Treat

y

as a constant

Take the constant out:

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

= e^{y} \frac{\partial}{\partial x} (2 x + 5 y)

Apply the Sum/Difference Rule:

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

= e^{y} (\frac{\partial}{\partial x} (2 x) + \frac{\partial}{\partial x} (5 y))

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (5 y) = 0

= e^{y} (2 + 0)

Simplify

= 2 e^{y}

\frac{\partial}{\partial x} (x + y - x y)

\int_{0}^{8} (x + 1)^{2} d x

y = arcsin (\frac{1}{x ^{5}})

x \to 0 lim (\frac{ln ( 1 - 6 x )}{x})

x \to - 8 lim (\frac{∣ x + 8 ∣}{x + 8})

What is (\partial)/(\partial x)((2x+5y)e^y) ?
The answer to (\partial)/(\partial x)((2x+5y)e^y) is 2e^y