What is (\partial)/(\partial y)((2x-5y)^2) ?

The answer to (\partial)/(\partial y)((2x-5y)^2) is -10(2x-5y)

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(\partial)/(\partial y)((2x-5y)^2)

\frac{\partial}{\partial y} ((2 x - 5 y)^{2})

- 10 (2 x - 5 y)

Solution steps

\frac{\partial}{\partial y} ((2 x - 5 y)^{2})

Treat

x

as a constant

Apply the chain rule:

2 (2 x - 5 y) \frac{\partial}{\partial y} (2 x - 5 y)

= 2 (2 x - 5 y) \frac{\partial}{\partial y} (2 x - 5 y)

\frac{\partial}{\partial y} (2 x - 5 y) = - 5

= 2 (2 x - 5 y) (- 5)

Simplify

= - 10 (2 x - 5 y)

(10 y^{2} - x y) d x + (x^{2}) d y = 0

\int 2 x (x^{2} + 3)^{2} d x

24 y^{^{''}} + 12 y^{^{'}} = 0, y (3) = - 3, y^{^{'}} (- 4) = 4

(2 x + 9)^{2}

\int \frac{tan ( x )}{1 - sin ^{2} ( x )} d x

What is (\partial)/(\partial y)((2x-5y)^2) ?
The answer to (\partial)/(\partial y)((2x-5y)^2) is -10(2x-5y)