What is (\partial)/(\partial x)(7e^y-4ye^x) ?

The answer to (\partial)/(\partial x)(7e^y-4ye^x) is -4e^xy

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(\partial)/(\partial x)(7e^y-4ye^x)

\frac{\partial}{\partial x} (7 e^{y} - 4 y e^{x})

- 4 e^{x} y

Solution steps

\frac{\partial}{\partial x} (7 e^{y} - 4 y e^{x})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (7 e^{y}) - \frac{\partial}{\partial x} (4 y e^{x})

\frac{\partial}{\partial x} (7 e^{y}) = 0

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

= 0 - 4 y e^{x}

Simplify

= - 4 e^{x} y

sin (9 x)

\frac{d}{d x} (e^{m x} m)

\frac{\partial}{\partial y} (x + y + z)

x \to - 2 lim (x - 2)

x, at x = 4

What is (\partial)/(\partial x)(7e^y-4ye^x) ?
The answer to (\partial)/(\partial x)(7e^y-4ye^x) is -4e^xy