What is (\partial)/(\partial x)((7x+y)(e^x)) ?

The answer to (\partial)/(\partial x)((7x+y)(e^x)) is 7e^x+e^x(7x+y)

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(\partial)/(\partial x)((7x+y)(e^x))

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

7 e^{x} + e^{x} (7 x + y)

Solution steps

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

Treat

y

as a constant

Apply the Product Rule:

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

f = 7 x + y, g = e^{x}

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

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

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

= 7 e^{x} + e^{x} (7 x + y)

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