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

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

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (5 y) = 0

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

= 0 - 3 y^{2} x^{2}

Simplify

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

\frac{d}{d x} (5 x^{2} sin (x) - x)

\frac{d}{d x} (cos (7))

x y^{^{'}} + y = - 4 x y^{2}

x \to 3 - lim (\frac{4 - x}{x - 3})

\int_{0}^{10} 1 + x d x

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