What is (\partial)/(\partial y)(4x^3y^2+2) ?

The answer to (\partial)/(\partial y)(4x^3y^2+2) is 8x^3y

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(\partial)/(\partial y)(4x^3y^2+2)

\frac{\partial}{\partial y} (4 x^{3} y^{2} + 2)

8 x^{3} y

Solution steps

\frac{\partial}{\partial y} (4 x^{3} y^{2} + 2)

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial y} (4 x^{3} y^{2}) + \frac{\partial}{\partial y} (2)

\frac{\partial}{\partial y} (4 x^{3} y^{2}) = 8 x^{3} y

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

= 8 x^{3} y + 0

Simplify

= 8 x^{3} y

x^{2} y^{^{''}} + x y^{^{'}} - 9 y = x^{3} + 1

n = 0 \sum \infty (1 + \frac{2}{n})^{3 n}

\frac{d}{d x} (x^{a} (1 - x)^{b})

x \to - 8 lim (\frac{- 5 x}{x + 8})

\int \frac{v}{0.122 - 0.0007 v ^{2}} d v

What is (\partial)/(\partial y)(4x^3y^2+2) ?
The answer to (\partial)/(\partial y)(4x^3y^2+2) is 8x^3y