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

The answer to (\partial)/(\partial x)((5x^3y+4y^5)^3) is 45x^2y(5x^3y+4y^5)^2

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

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

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

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

\frac{\partial}{\partial x} (5 x^{3} y + 4 y^{5}) = 15 y x^{2}

= 3 (5 x^{3} y + 4 y^{5})^{2} \cdot 15 y x^{2}

Simplify

= 45 x^{2} y (5 x^{3} y + 4 y^{5})^{2}

What is (\partial)/(\partial x)((5x^3y+4y^5)^3) ?
The answer to (\partial)/(\partial x)((5x^3y+4y^5)^3) is 45x^2y(5x^3y+4y^5)^2