What is (\partial)/(\partial x)(-45xy-5x^2y-5xy^2) ?

The answer to (\partial)/(\partial x)(-45xy-5x^2y-5xy^2) is -45y-10yx-5y^2

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(\partial)/(\partial x)(-45xy-5x^2y-5xy^2)

\frac{\partial}{\partial x} (- 45 x y - 5 x^{2} y - 5 x y^{2})

- 45 y - 10 y x - 5 y^{2}

Solution steps

\frac{\partial}{\partial x} (- 45 x y - 5 x^{2} y - 5 x y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= - \frac{\partial}{\partial x} (45 x y) - \frac{\partial}{\partial x} (5 x^{2} y) - \frac{\partial}{\partial x} (5 x y^{2})

\frac{\partial}{\partial x} (45 x y) = 45 y

\frac{\partial}{\partial x} (5 x^{2} y) = 10 y x

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

= - 45 y - 10 y x - 5 y^{2}

- x^{2} + 12 x - 32

x \to - 2 lim (∣ x - 2 ∣)

\int (4) d x

\frac{d}{d x} \frac{( x ^{2} - 4 ) ^{\frac{3}{2}}}{6}

n = 0 \sum \infty π

What is (\partial)/(\partial x)(-45xy-5x^2y-5xy^2) ?
The answer to (\partial)/(\partial x)(-45xy-5x^2y-5xy^2) is -45y-10yx-5y^2