What is (\partial)/(\partial y)(x^4y+xz-yz^2-7) ?

The answer to (\partial)/(\partial y)(x^4y+xz-yz^2-7) is x^4-z^2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(x^4y+xz-yz^2-7)

\frac{\partial}{\partial y} (x^{4} y + x z - y z^{2} - 7)

x^{4} - z^{2}

Solution steps

\frac{\partial}{\partial y} (x^{4} y + x z - y z^{2} - 7)

Treat

x, z

as constants

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{4} y) + \frac{\partial}{\partial y} (x z) - \frac{\partial}{\partial y} (y z^{2}) - \frac{\partial}{\partial y} (7)

\frac{\partial}{\partial y} (x^{4} y) = x^{4}

\frac{\partial}{\partial y} (x z) = 0

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

\frac{\partial}{\partial y} (7) = 0

= x^{4} + 0 - z^{2} - 0

Simplify

= x^{4} - z^{2}

\frac{d y}{d x} = e^{6 y} e^{6 x}

\frac{d y}{d x} = y (y^{5} x + 2)

1 - 4 x^{2} y^{^{'}} = x

\frac{x}{2}

x \to 0 lim (x^{11 x})

What is (\partial)/(\partial y)(x^4y+xz-yz^2-7) ?
The answer to (\partial)/(\partial y)(x^4y+xz-yz^2-7) is x^4-z^2