What is (\partial)/(\partial x)(x^6y^5+2x^9y) ?

The answer to (\partial)/(\partial x)(x^6y^5+2x^9y) is 6y^5x^5+18yx^8

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(\partial)/(\partial x)(x^6y^5+2x^9y)

\frac{\partial}{\partial x} (x^{6} y^{5} + 2 x^{9} y)

6 y^{5} x^{5} + 18 y x^{8}

Solution steps

\frac{\partial}{\partial x} (x^{6} y^{5} + 2 x^{9} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{6} y^{5}) + \frac{\partial}{\partial x} (2 x^{9} y)

\frac{\partial}{\partial x} (x^{6} y^{5}) = 6 y^{5} x^{5}

\frac{\partial}{\partial x} (2 x^{9} y) = 18 y x^{8}

= 6 y^{5} x^{5} + 18 y x^{8}

What is (\partial)/(\partial x)(x^6y^5+2x^9y) ?
The answer to (\partial)/(\partial x)(x^6y^5+2x^9y) is 6y^5x^5+18yx^8