What is (\partial)/(\partial x)(2xy+y^2+1) ?

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

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(\partial)/(\partial x)(2xy+y^2+1)

\frac{\partial}{\partial x} (2 x y + y^{2} + 1)

2 y

Solution steps

\frac{\partial}{\partial x} (2 x y + y^{2} + 1)

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} (y^{2}) + \frac{\partial}{\partial x} (1)

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

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

\frac{\partial}{\partial x} (1) = 0

= 2 y + 0 + 0

Simplify

= 2 y

\int \frac{3}{x ^{2}} + 4 x d x

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

\frac{1}{2} x^{2}, x^{2} - 3 x

\int (x - x^{2}) d x

x \to 0 lim (- e^{\frac{1}{x}})

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