What is (\partial)/(\partial x)((z)(z^4+z^2x^2-6)) ?

The answer to (\partial)/(\partial x)((z)(z^4+z^2x^2-6)) is 2z^3x

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)((z)(z^4+z^2x^2-6))

\frac{\partial}{\partial x} ((z) (z^{4} + z^{2} x^{2} - 6))

2 z^{3} x

Solution steps

\frac{\partial}{\partial x} ((z) (z^{4} + z^{2} x^{2} - 6))

Treat

z

as a constant

Take the constant out:

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

= z \frac{\partial}{\partial x} (z^{4} + z^{2} x^{2} - 6)

Apply the Sum/Difference Rule:

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

= z (\frac{\partial}{\partial x} (z^{4}) + \frac{\partial}{\partial x} (z^{2} x^{2}) - \frac{\partial}{\partial x} (6))

\frac{\partial}{\partial x} (z^{4}) = 0

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

\frac{\partial}{\partial x} (6) = 0

= z (0 + 2 z^{2} x - 0)

Simplify

z (0 + 2 z^{2} x - 0) : 2 z^{3} x

= 2 z^{3} x

(x^{2} + 35) \cdot (x^{2} - 35)

tan^{2} (a) \cdot (2 cos^{2} (a) + sin^{2} (a) - 1)

30 + 42

ln^{4} (x - 3) (x^{3} + 1)^{5} (2 cos (x) - 3)

P (- 4, 7) y Q (- 10, - 2)

What is (\partial)/(\partial x)((z)(z^4+z^2x^2-6)) ?
The answer to (\partial)/(\partial x)((z)(z^4+z^2x^2-6)) is 2z^3x