What is (\partial)/(\partial x)(sqrt(5+2x+3xy^2)) ?

The answer to (\partial)/(\partial x)(sqrt(5+2x+3xy^2)) is (3y^2+2)/(2sqrt(5+2x+3xy^2))

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(\partial)/(\partial x)(sqrt(5+2x+3xy^2))

\frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2})

\frac{3 y ^{2} + 2}{2 5 + 2 x + 3 x y ^{2}}

Solution steps

\frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2})

Treat

y

as a constant

Apply the chain rule:

\frac{1}{2 5 + 2 x + 3 x y ^{2}} \frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2})

= \frac{1}{2 5 + 2 x + 3 x y ^{2}} \frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2})

\frac{\partial}{\partial x} (5 + 2 x + 3 x y^{2}) = 3 y^{2} + 2

= \frac{1}{2 5 + 2 x + 3 x y ^{2}} (3 y^{2} + 2)

Simplify

\frac{1}{2 5 + 2 x + 3 x y ^{2}} (3 y^{2} + 2) : \frac{3 y ^{2} + 2}{2 5 + 2 x + 3 x y ^{2}}

= \frac{3 y ^{2} + 2}{2 5 + 2 x + 3 x y ^{2}}

What is (\partial)/(\partial x)(sqrt(5+2x+3xy^2)) ?
The answer to (\partial)/(\partial x)(sqrt(5+2x+3xy^2)) is (3y^2+2)/(2sqrt(5+2x+3xy^2))