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

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

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

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

2 e^{\frac{y}{2}} x

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= e^{\frac{y}{2}} (2 x + 0)

Simplify

= 2 e^{\frac{y}{2}} x

\int (4 - x^{2})^{\frac{3}{2}} d x

(\frac{x + 1}{x - 1})^{^{'}}

\frac{d y}{d t} = 5 y

\int x + x d x

y = \frac{2 x ^{5} + 8}{x ^{3}}

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