What is (\partial)/(\partial x)(sqrt(3x+2xy^2)) ?

The answer to (\partial)/(\partial x)(sqrt(3x+2xy^2)) is (3+2y^2)/(2sqrt(3x+2xy^2))

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(\partial)/(\partial x)(sqrt(3x+2xy^2))

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

\frac{3 + 2 y ^{2}}{2 3 x + 2 x y ^{2}}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 3 x + 2 x y ^{2}} \frac{\partial}{\partial x} (3 x + 2 x y^{2})

= \frac{1}{2 3 x + 2 x y ^{2}} \frac{\partial}{\partial x} (3 x + 2 x y^{2})

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

= \frac{1}{2 3 x + 2 x y ^{2}} (3 + 2 y^{2})

Simplify

\frac{1}{2 3 x + 2 x y ^{2}} (3 + 2 y^{2}) : \frac{3 + 2 y ^{2}}{2 3 x + 2 x y ^{2}}

= \frac{3 + 2 y ^{2}}{2 3 x + 2 x y ^{2}}

\frac{d}{d x} (2 ln (1 + x^{2}) - 3^{x})

y = arccos (\frac{11}{x})

\int x e^{x} y d x

\int_{1}^{l n (x)} \frac{1}{t} d t

\int \frac{1}{x ^{\frac{2}{3}}} d x

What is (\partial)/(\partial x)(sqrt(3x+2xy^2)) ?
The answer to (\partial)/(\partial x)(sqrt(3x+2xy^2)) is (3+2y^2)/(2sqrt(3x+2xy^2))