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

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

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

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

4 (x + 2 y)

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= 2 (x + 2 y) \cdot 2

Simplify

= 4 (x + 2 y)

\frac{d}{d x} (\frac{e ^{x} - 2}{( 1 - e ^{- x} ) ^{2}})

\int \frac{( 5 x ^{2} )}{1 - 5 x ^{3}} d x

x \to 0 + lim (sin (\frac{π}{x}))

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

2 x^{2} y^{^{'}} = y^{^{'}} + 6 x e^{(- y)}

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