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

The answer to (\partial)/(\partial x)((y)(2x-3y)^3) is 6y(2x-3y)^2

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

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

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

Solution steps

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

Treat

y

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the chain rule:

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

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

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

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

Simplify

= 6 y (2 x - 3 y)^{2}

e^{2 x} (e^{x} + 1)

- 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

\frac{1}{2 ( x - 3 )}

\frac{( x - 1 ) ^{2}}{x - 2}

\frac{2 s + 26}{s ( s ^{2} + 4 s + 13 )}

What is (\partial)/(\partial x)((y)(2x-3y)^3) ?
The answer to (\partial)/(\partial x)((y)(2x-3y)^3) is 6y(2x-3y)^2