What is (\partial)/(\partial x)((z)(e^z-7xyz)) ?

The answer to (\partial)/(\partial x)((z)(e^z-7xyz)) is -7z^2y

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(\partial)/(\partial x)((z)(e^z-7xyz))

\frac{\partial}{\partial x} ((z) (e^{z} - 7 x yz))

- 7 z^{2} y

Solution steps

\frac{\partial}{\partial x} ((z) (e^{z} - 7 x yz))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (e^{z} - 7 x yz)

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (e^{z}) - \frac{\partial}{\partial x} (7 x yz))

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

\frac{\partial}{\partial x} (7 x yz) = 7 zy

= z (0 - 7 zy)

Simplify

z (0 - 7 zy) : - 7 z^{2} y

= - 7 z^{2} y

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

\frac{- 2 s ^{3} + 3 s ^{2} t - t ^{3}}{( s - t ) ^{5}}

2 x e^{- x} + (x^{2} - 3) (- e^{- x})

a e n (b x + c)

((- 1)^{k + 1} \cdot (k + 1)) 8

What is (\partial)/(\partial x)((z)(e^z-7xyz)) ?
The answer to (\partial)/(\partial x)((z)(e^z-7xyz)) is -7z^2y