What is (\partial)/(\partial x)(6x^5y^6+5x^4y^7) ?

The answer to (\partial)/(\partial x)(6x^5y^6+5x^4y^7) is 30y^6x^4+20y^7x^3

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(\partial)/(\partial x)(6x^5y^6+5x^4y^7)

\frac{\partial}{\partial x} (6 x^{5} y^{6} + 5 x^{4} y^{7})

30 y^{6} x^{4} + 20 y^{7} x^{3}

Solution steps

\frac{\partial}{\partial x} (6 x^{5} y^{6} + 5 x^{4} y^{7})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 x^{5} y^{6}) + \frac{\partial}{\partial x} (5 x^{4} y^{7})

\frac{\partial}{\partial x} (6 x^{5} y^{6}) = 30 y^{6} x^{4}

\frac{\partial}{\partial x} (5 x^{4} y^{7}) = 20 y^{7} x^{3}

= 30 y^{6} x^{4} + 20 y^{7} x^{3}

What is (\partial)/(\partial x)(6x^5y^6+5x^4y^7) ?
The answer to (\partial)/(\partial x)(6x^5y^6+5x^4y^7) is 30y^6x^4+20y^7x^3