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

The answer to (\partial)/(\partial x)(3x^7y^8+8x^5y^6) is 21y^8x^6+40y^6x^4

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

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

21 y^{8} x^{6} + 40 y^{6} x^{4}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (3 x^{7} y^{8}) = 21 y^{8} x^{6}

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

= 21 y^{8} x^{6} + 40 y^{6} x^{4}

\frac{d}{d x} (\frac{x ^{\frac{2}{3}}}{5 + x + x ^{4}})

\int 4 x + \frac{1}{4 x} d x

\int 5 x e^{- 2 x} d x

\frac{2}{s + 3}

\frac{s + 1}{( s ^{2} + 9 )}

What is (\partial)/(\partial x)(3x^7y^8+8x^5y^6) ?
The answer to (\partial)/(\partial x)(3x^7y^8+8x^5y^6) is 21y^8x^6+40y^6x^4