What is (\partial)/(\partial y)(xy^2e^y) ?

The answer to (\partial)/(\partial y)(xy^2e^y) is x(2ye^y+e^yy^2)

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(\partial)/(\partial y)(xy^2e^y)

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

x (2 y e^{y} + e^{y} y^{2})

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the Product Rule:

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

f = y^{2}, g = e^{y}

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

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

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

= x (2 y e^{y} + e^{y} y^{2})

f (x) = (5 x^{3} + 2)^{4}

\frac{d}{d x} (tan (arcsin (x)))

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

\int \frac{( 5 x - 12 )}{x ^{3} - 6 x ^{2} + 8 x} d x

x \to 1 - lim (\frac{3}{x ^{3} - 1})

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