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

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

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

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

e^{y} y^{2}

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the common derivative:

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

= y^{2} e^{y} \cdot 1

Simplify

= e^{y} y^{2}

y^{^{''}} - 4 y^{^{'}} + 8 = 0

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

\int \frac{1}{1 + z ^{2}} d z

t^{2} y^{^{''}} + 13 t y^{^{'}} + 36 y = 0

9 y^{^{''}} - 60 y^{^{'}} + 51 y = 0, y (0) = 1, y^{^{'}} (0) = 0

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