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

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

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

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

4 y^{3}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= 0 + 0 + 4 y^{3}

Simplify

= 4 y^{3}

y^{^{''}} + y = 2 x e^{x}

\frac{d}{d x} (ln (6 - x))

\frac{d}{d x} (\frac{( x ^{2} - 8 x + 15 )}{x ^{2} + 3 x + 2})

\frac{\partial}{\partial x} (4 x^{2} y^{3})

\int \frac{4 x}{4 x ^{4} + 9} d x

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