What is (\partial)/(\partial y)(x^3y^5-2x^2y+x) ?

The answer to (\partial)/(\partial y)(x^3y^5-2x^2y+x) is 5x^3y^4-2x^2

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(\partial)/(\partial y)(x^3y^5-2x^2y+x)

\frac{\partial}{\partial y} (x^{3} y^{5} - 2 x^{2} y + x)

5 x^{3} y^{4} - 2 x^{2}

Solution steps

\frac{\partial}{\partial y} (x^{3} y^{5} - 2 x^{2} y + x)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{3} y^{5}) - \frac{\partial}{\partial y} (2 x^{2} y) + \frac{\partial}{\partial y} (x)

\frac{\partial}{\partial y} (x^{3} y^{5}) = 5 x^{3} y^{4}

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

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

= 5 x^{3} y^{4} - 2 x^{2} + 0

Simplify

= 5 x^{3} y^{4} - 2 x^{2}

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What is (\partial)/(\partial y)(x^3y^5-2x^2y+x) ?
The answer to (\partial)/(\partial y)(x^3y^5-2x^2y+x) is 5x^3y^4-2x^2