What is (\partial)/(\partial y)(1+2xsqrt(y)) ?

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

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(\partial)/(\partial y)(1+2xsqrt(y))

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

\frac{x}{y}

Solution steps

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

Treat

x

as a constant

Apply the Sum/Difference Rule:

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

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

\frac{\partial}{\partial y} (1) = 0

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

= 0 + \frac{x}{y}

Simplify

= \frac{x}{y}

1 - e^{3 x^{2}}

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

\frac{2 s ^{2}}{s ^{4} - 1}

\int_{0}^{1} 2 x (x^{2} + 1)^{2} d x

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