What is (\partial)/(\partial x)((z)(9xyz-e^z)) ?

The answer to (\partial)/(\partial x)((z)(9xyz-e^z)) is 9z^2y

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(\partial)/(\partial x)((z)(9xyz-e^z))

\frac{\partial}{\partial x} ((z) (9 x yz - e^{z}))

9 z^{2} y

Solution steps

\frac{\partial}{\partial x} ((z) (9 x yz - e^{z}))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (9 x yz - e^{z})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (9 x yz) - \frac{\partial}{\partial x} (e^{z}))

\frac{\partial}{\partial x} (9 x yz) = 9 zy

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

= z (9 zy - 0)

Simplify

z (9 zy - 0) : 9 z^{2} y

= 9 z^{2} y

4 (3 - 3)

(x + 1) sin (x^{2})

(2 + 1)^{6}

(y - 1) (y + 4 + 4 y + 1)

\frac{( x + 1 ) ( x + 4 ) ( x - 2 ) ( x - 5 )}{( x + 2 ) ( x - 1 )}

What is (\partial)/(\partial x)((z)(9xyz-e^z)) ?
The answer to (\partial)/(\partial x)((z)(9xyz-e^z)) is 9z^2y