What is (\partial)/(\partial x)(6y^8x^5+49yx^6) ?

The answer to (\partial)/(\partial x)(6y^8x^5+49yx^6) is 30y^8x^4+294yx^5

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(\partial)/(\partial x)(6y^8x^5+49yx^6)

\frac{\partial}{\partial x} (6 y^{8} x^{5} + 49 y x^{6})

30 y^{8} x^{4} + 294 y x^{5}

Solution steps

\frac{\partial}{\partial x} (6 y^{8} x^{5} + 49 y x^{6})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (6 y^{8} x^{5}) + \frac{\partial}{\partial x} (49 y x^{6})

\frac{\partial}{\partial x} (6 y^{8} x^{5}) = 30 y^{8} x^{4}

\frac{\partial}{\partial x} (49 y x^{6}) = 294 y x^{5}

= 30 y^{8} x^{4} + 294 y x^{5}

What is (\partial)/(\partial x)(6y^8x^5+49yx^6) ?
The answer to (\partial)/(\partial x)(6y^8x^5+49yx^6) is 30y^8x^4+294yx^5