What is (\partial)/(\partial y)(x^4+x^2y+x+5) ?

The answer to (\partial)/(\partial y)(x^4+x^2y+x+5) is x^2

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(\partial)/(\partial y)(x^4+x^2y+x+5)

\frac{\partial}{\partial y} (x^{4} + x^{2} y + x + 5)

x^{2}

Solution steps

\frac{\partial}{\partial y} (x^{4} + x^{2} y + x + 5)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{4}) + \frac{\partial}{\partial y} (x^{2} y) + \frac{\partial}{\partial y} (x) + \frac{\partial}{\partial y} (5)

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

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

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

\frac{\partial}{\partial y} (5) = 0

= 0 + x^{2} + 0 + 0

Simplify

= x^{2}

sin (\frac{x - 3}{2 x})

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\frac{d}{d x} (ln (x^{6} - 1))

\frac{d}{d x} (e^{s i n (x)} cos (x))

What is (\partial)/(\partial y)(x^4+x^2y+x+5) ?
The answer to (\partial)/(\partial y)(x^4+x^2y+x+5) is x^2