What is (\partial)/(\partial x)(4+x+x^2y) ?

The answer to (\partial)/(\partial x)(4+x+x^2y) is 2xy+1

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(\partial)/(\partial x)(4+x+x^2y)

\frac{\partial}{\partial x} (4 + x + x^{2} y)

2 x y + 1

Solution steps

\frac{\partial}{\partial x} (4 + x + x^{2} y)

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (4) + \frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (x^{2} y)

\frac{\partial}{\partial x} (4) = 0

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

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

= 0 + 1 + 2 y x

Simplify

= 2 x y + 1

x \to 0 lim (\frac{4}{x})

\frac{d}{d x} (2 x^{2} - 6)

e^{- 3 s}

\frac{\partial}{\partial y} (3 y^{2} + 10 x y^{2})

\int \frac{1}{( x + 1 ) ^{2} ( x - 5 )} d x

What is (\partial)/(\partial x)(4+x+x^2y) ?
The answer to (\partial)/(\partial x)(4+x+x^2y) is 2xy+1