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

The answer to (\partial)/(\partial x)(x^4y-4x^5y^2) is 4yx^3-20y^2x^4

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

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

4 y x^{3} - 20 y^{2} x^{4}

Solution steps

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

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

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

= 4 y x^{3} - 20 y^{2} x^{4}

\frac{e ^{x} + 9 x}{3 x}

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

\int 2 sin (θ) d θ

f (x) = 2 x^{3} - 9 x^{2} - 24 x + 2

\frac{4}{3} π x^{3}

What is (\partial)/(\partial x)(x^4y-4x^5y^2) ?
The answer to (\partial)/(\partial x)(x^4y-4x^5y^2) is 4yx^3-20y^2x^4