What is (\partial)/(\partial x)((xy+1)^2) ?

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

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(\partial)/(\partial x)((xy+1)^2)

\frac{\partial}{\partial x} ((x y + 1)^{2})

2 (x y + 1) y

Solution steps

\frac{\partial}{\partial x} ((x y + 1)^{2})

Treat

y

as a constant

Apply the chain rule:

2 (x y + 1) \frac{\partial}{\partial x} (x y + 1)

= 2 (x y + 1) \frac{\partial}{\partial x} (x y + 1)

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

= 2 (x y + 1) y

\frac{d}{d x} (e^{c o t (x^{2})})

\frac{d y}{d x} = \frac{4 x y}{2 + x ^{2}}

(1 + x)^{- \frac{4}{5}}

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

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

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