What is (\partial)/(\partial y)((5x^3y+4y^5)^3) ?

The answer to (\partial)/(\partial y)((5x^3y+4y^5)^3) is 3(5x^3y+4y^5)^2(5x^3+20y^4)

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(\partial)/(\partial y)((5x^3y+4y^5)^3)

\frac{\partial}{\partial y} ((5 x^{3} y + 4 y^{5})^{3})

3 (5 x^{3} y + 4 y^{5})^{2} (5 x^{3} + 20 y^{4})

Solution steps

\frac{\partial}{\partial y} ((5 x^{3} y + 4 y^{5})^{3})

Treat

x

as a constant

Apply the chain rule:

3 (5 x^{3} y + 4 y^{5})^{2} \frac{\partial}{\partial y} (5 x^{3} y + 4 y^{5})

= 3 (5 x^{3} y + 4 y^{5})^{2} \frac{\partial}{\partial y} (5 x^{3} y + 4 y^{5})

\frac{\partial}{\partial y} (5 x^{3} y + 4 y^{5}) = 5 x^{3} + 20 y^{4}

= 3 (5 x^{3} y + 4 y^{5})^{2} (5 x^{3} + 20 y^{4})

x^{2} + 3 x - 2

\int_{- π}^{π} cos (3 x) sin (3 x) d x

x \to 0 lim (\frac{k}{x ( x + 1 )})

x \to 3 + lim (\frac{x + 1}{3 - x})

y = 2 x

What is (\partial)/(\partial y)((5x^3y+4y^5)^3) ?
The answer to (\partial)/(\partial y)((5x^3y+4y^5)^3) is 3(5x^3y+4y^5)^2(5x^3+20y^4)