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

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

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

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

x + 4 y^{3}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

= x + 0 + 4 y^{3}

Simplify

= x + 4 y^{3}

\int_{1}^{2} 4 x^{\frac{3}{2}} d x

\int cos (3 x) cos (x) d x

3 (1 + x^{2}) y^{^{'}} = 2 x y (y^{3} - 1)

f (t) = 2 - \frac{4}{t}, (4, 1)

\frac{d}{d x} (x^{2} + \frac{a ^{4}}{x ^{2}})

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