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

The answer to (\partial)/(\partial x)((z)(e^z-x^2yz)) is -2z^2xy

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(\partial)/(\partial x)((z)(e^z-x^2yz))

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

- 2 z^{2} x y

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (x^{2} yz) = 2 zy x

= z (0 - 2 zy x)

Simplify

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

= - 2 z^{2} x y

e^{4000 t} (1199753 cos (2000 t) + b sin (2000 t))

\frac{K}{( s + 1 ) ( s + 3 ) ( s + 6 )}

\frac{e ^{z t} ( t ( z - i ) - 2 )}{( z - i ) ^{3}}

(x + 1) y^{2} + \frac{ln ( y )}{x}

(a + c - cos (x) b)^{2}

What is (\partial)/(\partial x)((z)(e^z-x^2yz)) ?
The answer to (\partial)/(\partial x)((z)(e^z-x^2yz)) is -2z^2xy