What is (\partial)/(\partial y)(6y^2e^{6xy}) ?

The answer to (\partial)/(\partial y)(6y^2e^{6xy}) is 6(2ye^{6xy}+e^{6xy}*6xy^2)

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(\partial)/(\partial y)(6y^2e^{6xy})

\frac{\partial}{\partial y} (6 y^{2} e^{6 x y})

6 (2 y e^{6 x y} + e^{6 x y} \cdot 6 x y^{2})

Solution steps

\frac{\partial}{\partial y} (6 y^{2} e^{6 x y})

Treat

x

as a constant

Take the constant out:

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

= 6 \frac{\partial}{\partial y} (y^{2} e^{6 x y})

Apply the Product Rule:

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

f = y^{2}, g = e^{6 x y}

= 6 (\frac{\partial}{\partial y} (y^{2}) e^{6 x y} + \frac{\partial}{\partial y} (e^{6 x y}) y^{2})

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

\frac{\partial}{\partial y} (e^{6 x y}) = e^{6 x y} \cdot 6 x

= 6 (2 y e^{6 x y} + e^{6 x y} \cdot 6 x y^{2})

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What is (\partial)/(\partial y)(6y^2e^{6xy}) ?
The answer to (\partial)/(\partial y)(6y^2e^{6xy}) is 6(2ye^{6xy}+e^{6xy}*6xy^2)