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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(x^3+2xy-y^2)

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

3 x^{2} + 2 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

Simplify

= 3 x^{2} + 2 y

y = \frac{3}{4 x ^{5}}

x \to 0 lim (\frac{sin ( x )}{6 x})

y = 5 + 4 x^{2} - 2 x^{3}, (2, 5)

x^{^{''}} + a x = 0

16 y^{^{''}} + 24 y^{^{'}} + 9 y = 0

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