What is (\partial)/(\partial x)(x^6y-4x^5y^2) ?

The answer to (\partial)/(\partial x)(x^6y-4x^5y^2) is 6yx^5-20y^2x^4

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(\partial)/(\partial x)(x^6y-4x^5y^2)

\frac{\partial}{\partial x} (x^{6} y - 4 x^{5} y^{2})

6 y x^{5} - 20 y^{2} x^{4}

Solution steps

\frac{\partial}{\partial x} (x^{6} y - 4 x^{5} y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (x^{6} y) - \frac{\partial}{\partial x} (4 x^{5} y^{2})

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

\frac{\partial}{\partial x} (4 x^{5} y^{2}) = 20 y^{2} x^{4}

= 6 y x^{5} - 20 y^{2} x^{4}

e^{3 x} - e^{2 x}

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

\int n e^{- n y} sin (n x) d x

x e^{x^{3}}

\int \frac{1}{0.15 p + 20} d p

What is (\partial)/(\partial x)(x^6y-4x^5y^2) ?
The answer to (\partial)/(\partial x)(x^6y-4x^5y^2) is 6yx^5-20y^2x^4