What is (\partial)/(\partial y)(x^5+x^2y+x+1) ?

The answer to (\partial)/(\partial y)(x^5+x^2y+x+1) is x^2

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(\partial)/(\partial y)(x^5+x^2y+x+1)

\frac{\partial}{\partial y} (x^{5} + x^{2} y + x + 1)

x^{2}

Solution steps

\frac{\partial}{\partial y} (x^{5} + x^{2} y + x + 1)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{5}) + \frac{\partial}{\partial y} (x^{2} y) + \frac{\partial}{\partial y} (x) + \frac{\partial}{\partial y} (1)

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

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

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

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

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

Simplify

= x^{2}

\frac{\partial}{\partial α} (sin (α) cos (β))

\int \frac{1}{x ^{2} 9 - 4 x ^{2}} d x

\frac{d}{d y} (\frac{x}{x + y})

8 x - x^{2} (1.7)

x \to 0 lim (\frac{x}{- 2 x ^{5} + 15 x})

What is (\partial)/(\partial y)(x^5+x^2y+x+1) ?
The answer to (\partial)/(\partial y)(x^5+x^2y+x+1) is x^2