What is (\partial)/(\partial x)(8x^5y^6+6x^4y^8) ?

The answer to (\partial)/(\partial x)(8x^5y^6+6x^4y^8) is 40y^6x^4+24y^8x^3

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(\partial)/(\partial x)(8x^5y^6+6x^4y^8)

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

40 y^{6} x^{4} + 24 y^{8} x^{3}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (8 x^{5} y^{6}) = 40 y^{6} x^{4}

\frac{\partial}{\partial x} (6 x^{4} y^{8}) = 24 y^{8} x^{3}

= 40 y^{6} x^{4} + 24 y^{8} x^{3}

6 x^{- 4}

\frac{\partial}{\partial x} (5 y^{\frac{1}{4}} x^{\frac{1}{2}})

\int x^{3} 4 + x^{4} d x

\frac{d y}{d x} = y (3 - y)

What is (\partial)/(\partial x)(8x^5y^6+6x^4y^8) ?
The answer to (\partial)/(\partial x)(8x^5y^6+6x^4y^8) is 40y^6x^4+24y^8x^3