What is (\partial)/(\partial x)((z)(z^2-5x^2+y^2)) ?

The answer to (\partial)/(\partial x)((z)(z^2-5x^2+y^2)) is -10zx

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(\partial)/(\partial x)((z)(z^2-5x^2+y^2))

\frac{\partial}{\partial x} ((z) (z^{2} - 5 x^{2} + y^{2}))

- 10 z x

Solution steps

\frac{\partial}{\partial x} ((z) (z^{2} - 5 x^{2} + y^{2}))

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} (z^{2} - 5 x^{2} + y^{2})

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (z^{2}) - \frac{\partial}{\partial x} (5 x^{2}) + \frac{\partial}{\partial x} (y^{2}))

\frac{\partial}{\partial x} (z^{2}) = 0

\frac{\partial}{\partial x} (5 x^{2}) = 10 x

\frac{\partial}{\partial x} (y^{2}) = 0

= z (0 - 10 x + 0)

Simplify

= - 10 z x

(4 x^{3} e^{x}) (x^{2} + 1)

(x + \frac{1}{2}) (x - 1) (x - \frac{3}{4})

2 (sin (t)) (t) (7 - t^{2})

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

What is (\partial)/(\partial x)((z)(z^2-5x^2+y^2)) ?
The answer to (\partial)/(\partial x)((z)(z^2-5x^2+y^2)) is -10zx