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

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

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

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

4 x^{3} - 4 y

Solution steps

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

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} (4 x y) = 4 y

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

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

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

Simplify

= 4 x^{3} - 4 y

y^{^{''}} + 4 y = 0

\int x sin (1 - 2 x) d x

\int \frac{2 - x}{x ^{2} - 2 x + 1} d x

x^{3}, x

7 x^{3} e^{x}

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