What is (\partial)/(\partial y)(x^4y-3x^5y^2) ?

The answer to (\partial)/(\partial y)(x^4y-3x^5y^2) is x^4-6x^5y

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(\partial)/(\partial y)(x^4y-3x^5y^2)

\frac{\partial}{\partial y} (x^{4} y - 3 x^{5} y^{2})

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

Solution steps

\frac{\partial}{\partial y} (x^{4} y - 3 x^{5} y^{2})

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (x^{4} y) - \frac{\partial}{\partial y} (3 x^{5} y^{2})

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

\frac{\partial}{\partial y} (3 x^{5} y^{2}) = 6 x^{5} y

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

x \to 1 lim (x + 1)

\int x ln (3 x) d x

\frac{d}{d x} (x (x - 15)^{2})

\int e^{s i n (x)} cos (x) d x

What is (\partial)/(\partial y)(x^4y-3x^5y^2) ?
The answer to (\partial)/(\partial y)(x^4y-3x^5y^2) is x^4-6x^5y