What is (\partial)/(\partial x)(4xy-x^4-y^4+1) ?

The answer to (\partial)/(\partial x)(4xy-x^4-y^4+1) is 4y-4x^3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(\partial)/(\partial x)(4xy-x^4-y^4+1)

\frac{\partial}{\partial x} (4 x y - x^{4} - y^{4} + 1)

4 y - 4 x^{3}

Solution steps

\frac{\partial}{\partial x} (4 x y - x^{4} - y^{4} + 1)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4 x y) - \frac{\partial}{\partial x} (x^{4}) - \frac{\partial}{\partial x} (y^{4}) + \frac{\partial}{\partial x} (1)

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

\frac{\partial}{\partial x} (x^{4}) = 4 x^{3}

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

\frac{\partial}{\partial x} (1) = 0

= 4 y - 4 x^{3} - 0 + 0

Simplify

= 4 y - 4 x^{3}

\int_{0}^{x} e^{- t^{2}} d t

\frac{x + 1}{4 x ^{2} + 12 x + 2}

\frac{d}{d x} (3 arcsin (x^{2}))

\int_{1}^{2} 4^{x} d x

4 x^{2}, \frac{x}{2}

What is (\partial)/(\partial x)(4xy-x^4-y^4+1) ?
The answer to (\partial)/(\partial x)(4xy-x^4-y^4+1) is 4y-4x^3