What is (\partial)/(\partial y)((2x-3y)^3) ?

The answer to (\partial)/(\partial y)((2x-3y)^3) is -9(2x-3y)^2

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(\partial)/(\partial y)((2x-3y)^3)

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

- 9 (2 x - 3 y)^{2}

Solution steps

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

Treat

x

as a constant

Apply the chain rule:

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

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

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

= 3 (2 x - 3 y)^{2} (- 3)

Simplify

= - 9 (2 x - 3 y)^{2}

\int - csc (x) cot (x) d x

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

(x + 6)^{2}

\frac{d}{d x} (\frac{5}{x ^{5}} + \frac{3}{x ^{2}})

What is (\partial)/(\partial y)((2x-3y)^3) ?
The answer to (\partial)/(\partial y)((2x-3y)^3) is -9(2x-3y)^2