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

The answer to (\partial)/(\partial y)(x^2e^{5y}) is x^2e^{5y}*5

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

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

x^{2} e^{5 y} \cdot 5

Solution steps

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

Treat

x

as a constant

Take the constant out:

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

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

Apply the chain rule:

e^{5 y} \frac{\partial}{\partial y} (5 y)

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

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

= x^{2} e^{5 y} \cdot 5

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