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

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

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

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

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

\frac{d}{d x} ((4 x^{3} + 1)^{3})

5 - x^{2}, sin (x), - 2.384677, 2.0252116

\int \frac{1 - sin ( x )}{cos ( x )} d x

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

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