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

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

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

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

- 3 y^{3} + 2 y

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

\frac{\partial}{\partial x} (5 y^{2}) = 0

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

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

Simplify

= - 3 y^{3} + 2 y

x \to 1 lim (e^{5 x^{4} - 5 x})

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

x \to 0 lim (\frac{( sin ( 5 x ) )}{x})

\int \frac{cos ( t )}{t} d t

\frac{d y}{d x} = x (y - 1)^{2}

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