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

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

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(\partial)/(\partial y)(sqrt(1+xy^2))

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} (ln (x^{11}))

\frac{\partial}{\partial x} (x^{2} y^{3} (6 - x - y))

\frac{d}{d x} (x^{15})

y^{^{'}} = sin (x) y + e^{x}

\frac{\partial}{\partial θ} (\frac{cos ( θ )}{r ( θ )})

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