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

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

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

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

y^{2}

Solution steps

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

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

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

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

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

= y^{2} + 0

Simplify

= y^{2}

\frac{d y}{d x} + y^{3} x + 5 y = 0

6 x (\frac{d y}{d x}) = 2 x e^{x} - 6 y + 6 x^{2}

\int_{0}^{1} 4 x y d y

\int \frac{sin ( 6 e ^{- 5 x} )}{e ^{5 x}} d x

h \to 0 lim (\frac{( 2 + h ) ^{2} - 4}{h})

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