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

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

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(\partial)/(\partial x)((z)(x^2e^y-yze^x))

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

z (2 e^{y} x - yz e^{x})

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

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

= z (2 e^{y} x - yz e^{x})

\frac{( 3 x ^{2} - 1 )}{( 3 x ^{2} + 1 ) ^{2}}

\frac{( 2 + x ) ^{10}}{1024}

(sin (t) - e^{3 t}) u (t - π)

\frac{( n ^{2} + 2 n + 3 )}{( n + 1 ) ^{2}}

\frac{1}{s ^{2} ( s + 5 )}

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