What is (\partial)/(\partial y)((xy^2+x^3)^4) ?

The answer to (\partial)/(\partial y)((xy^2+x^3)^4) is 8xy(xy^2+x^3)^3

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(\partial)/(\partial y)((xy^2+x^3)^4)

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

8 x y (x y^{2} + x^{3})^{3}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

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

Simplify

= 8 x y (x y^{2} + x^{3})^{3}

\frac{d}{d x} (4 ln (x) + 2 cos (x) + x^{4})

f (x) = 5 x^{2} - 5 x, at x = 3

\int \frac{arctan ( \frac{x}{2} )}{4 + x ^{2}} d x

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

\int (cosh (x))^{3} d x

What is (\partial)/(\partial y)((xy^2+x^3)^4) ?
The answer to (\partial)/(\partial y)((xy^2+x^3)^4) is 8xy(xy^2+x^3)^3