What is (\partial)/(\partial y)(x^3-6xy+y^3) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial y)(x^3-6xy+y^3)

\frac{\partial}{\partial y} (x^{3} - 6 x y + y^{3})

3 y^{2} - 6 x

Solution steps

\frac{\partial}{\partial y} (x^{3} - 6 x y + y^{3})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{3}) - \frac{\partial}{\partial y} (6 x y) + \frac{\partial}{\partial y} (y^{3})

\frac{\partial}{\partial y} (x^{3}) = 0

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

\frac{\partial}{\partial y} (y^{3}) = 3 y^{2}

= 0 - 6 x + 3 y^{2}

Simplify

= 3 y^{2} - 6 x

x \to 5 lim (2 x)

f (x) = 4 x^{2} + 12 x + 3, at x = - 2

\int 5 x^{4} - 8 x^{5} d x

y^{^{''}} = a \cdot y

(x^{2} - 6 x + 10) 25 - x^{2}

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