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

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

Popular >

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

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

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

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial y} (3 x + 2 x y^{2}) = 4 x y

= \frac{1}{2 3 x + 2 x y ^{2}} \cdot 4 x y

Simplify

\frac{1}{2 3 x + 2 x y ^{2}} \cdot 4 x y : \frac{2 x y}{3 x + 2 x y ^{2}}

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

\int \frac{4}{( x ^{2} + 5 x - 14 )} d x

x \to 2 lim (2 x^{2} - 3)

x \to - 1 + lim (\frac{1}{x ^{2} - 1})

\int \frac{2 x ^{3} + x ^{2} - 21 x + 24}{x ^{2} + 2 x - 8} d x

\int 9 x^{2} - 4 d x

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