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

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

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

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

2 e^{x y + 6} y

Solution steps

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

Treat

y

as a constant

Take the constant out:

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

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

Apply the chain rule:

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

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

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

= 2 e^{x y + 6} y

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