What is (\partial)/(\partial x)(x^3y^5+9x^5y) ?

The answer to (\partial)/(\partial x)(x^3y^5+9x^5y) is 3y^5x^2+45yx^4

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(\partial)/(\partial x)(x^3y^5+9x^5y)

\frac{\partial}{\partial x} (x^{3} y^{5} + 9 x^{5} y)

3 y^{5} x^{2} + 45 y x^{4}

Solution steps

\frac{\partial}{\partial x} (x^{3} y^{5} + 9 x^{5} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{3} y^{5}) + \frac{\partial}{\partial x} (9 x^{5} y)

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

\frac{\partial}{\partial x} (9 x^{5} y) = 45 y x^{4}

= 3 y^{5} x^{2} + 45 y x^{4}

What is (\partial)/(\partial x)(x^3y^5+9x^5y) ?
The answer to (\partial)/(\partial x)(x^3y^5+9x^5y) is 3y^5x^2+45yx^4