What is (\partial)/(\partial x)(4(e^x-x^2y)) ?

The answer to (\partial)/(\partial x)(4(e^x-x^2y)) is 4(e^x-2yx)

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(\partial)/(\partial x)(4(e^x-x^2y))

\frac{\partial}{\partial x} (4 (e^{x} - x^{2} y))

4 (e^{x} - 2 y x)

Solution steps

\frac{\partial}{\partial x} (4 (e^{x} - x^{2} y))

Treat

y

as a constant

Take the constant out:

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

= 4 \frac{\partial}{\partial x} (e^{x} - x^{2} y)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 4 (\frac{\partial}{\partial x} (e^{x}) - \frac{\partial}{\partial x} (x^{2} y))

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

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

= 4 (e^{x} - 2 y x)

What is (\partial)/(\partial x)(4(e^x-x^2y)) ?
The answer to (\partial)/(\partial x)(4(e^x-x^2y)) is 4(e^x-2yx)