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

The answer to (\partial)/(\partial x)(x-y^2+3xy) is 3y+1

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

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

3 y + 1

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial x} (x) = 1

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

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

= 1 - 0 + 3 y

Simplify

= 3 y + 1

\int (\frac{1}{x ^{2} + 9}) d x

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

\frac{d}{d x} (\frac{1}{2 x + 2})

(- 3.3) (5.9)

\frac{\partial}{\partial y} (e^{2 y})

What is (\partial)/(\partial x)(x-y^2+3xy) ?
The answer to (\partial)/(\partial x)(x-y^2+3xy) is 3y+1