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

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

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

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

y + 1

Solution steps

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

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

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

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

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

\frac{\partial}{\partial x} (3) = 0

= 1 + 0 + y + 0

Simplify

= y + 1

y = x^{3} - 3

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

tan (θ) d r + 2 r d θ = 0

sin (x) ln (6 x)

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