What is (\partial)/(\partial x)(3x^8y^7+6x^5y^4) ?

The answer to (\partial)/(\partial x)(3x^8y^7+6x^5y^4) is 24y^7x^7+30y^4x^4

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(\partial)/(\partial x)(3x^8y^7+6x^5y^4)

\frac{\partial}{\partial x} (3 x^{8} y^{7} + 6 x^{5} y^{4})

24 y^{7} x^{7} + 30 y^{4} x^{4}

Solution steps

\frac{\partial}{\partial x} (3 x^{8} y^{7} + 6 x^{5} y^{4})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (3 x^{8} y^{7}) + \frac{\partial}{\partial x} (6 x^{5} y^{4})

\frac{\partial}{\partial x} (3 x^{8} y^{7}) = 24 y^{7} x^{7}

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

= 24 y^{7} x^{7} + 30 y^{4} x^{4}

\int \frac{11 x ^{3}}{9 + x ^{2}} d x

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\frac{d}{d x} (\frac{x ^{3}}{3} + \frac{1}{4 x})

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What is (\partial)/(\partial x)(3x^8y^7+6x^5y^4) ?
The answer to (\partial)/(\partial x)(3x^8y^7+6x^5y^4) is 24y^7x^7+30y^4x^4