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

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

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

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

2 x + 3 y + 5

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

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

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

= 2 x + 0 + 3 y + 5

Simplify

= 2 x + 3 y + 5

x^{2} y^{^{'}} + (2 - y) = 0

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

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

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

\frac{\partial}{\partial x} (7 x y^{3} + 5)

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