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

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

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(\partial)/(\partial x)(sqrt(1+xy))

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

\frac{y}{2 1 + x y}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= \frac{1}{2 1 + x y} y

Simplify

\frac{1}{2 1 + x y} y : \frac{y}{2 1 + x y}

= \frac{y}{2 1 + x y}

(5.12) (- 3.4)

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

\frac{2}{x - 2}

y^{^{'}} + e^{- x} y = e^{e - x}

\int_{0}^{4} x - \frac{1}{2} x d x

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