What is (\partial)/(\partial x)(7e^{xy+8}) ?

The answer to (\partial)/(\partial x)(7e^{xy+8}) is 7e^{xy+8}y

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(\partial)/(\partial x)(7e^{xy+8})

\frac{\partial}{\partial x} (7 e^{x y + 8})

7 e^{x y + 8} y

Solution steps

\frac{\partial}{\partial x} (7 e^{x y + 8})

Treat

y

as a constant

Take the constant out:

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

= 7 \frac{\partial}{\partial x} (e^{x y + 8})

Apply the chain rule:

e^{x y + 8} \frac{\partial}{\partial x} (x y + 8)

= e^{x y + 8} \frac{\partial}{\partial x} (x y + 8)

\frac{\partial}{\partial x} (x y + 8) = y

= 7 e^{x y + 8} y

What is (\partial)/(\partial x)(7e^{xy+8}) ?
The answer to (\partial)/(\partial x)(7e^{xy+8}) is 7e^{xy+8}y