What is (\partial)/(\partial x)((x^2+9x-4y)^6) ?

The answer to (\partial)/(\partial x)((x^2+9x-4y)^6) is 6(x^2+9x-4y)^5(2x+9)

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(\partial)/(\partial x)((x^2+9x-4y)^6)

\frac{\partial}{\partial x} ((x^{2} + 9 x - 4 y)^{6})

6 (x^{2} + 9 x - 4 y)^{5} (2 x + 9)

Solution steps

\frac{\partial}{\partial x} ((x^{2} + 9 x - 4 y)^{6})

Treat

y

as a constant

Apply the chain rule:

6 (x^{2} + 9 x - 4 y)^{5} \frac{\partial}{\partial x} (x^{2} + 9 x - 4 y)

= 6 (x^{2} + 9 x - 4 y)^{5} \frac{\partial}{\partial x} (x^{2} + 9 x - 4 y)

\frac{\partial}{\partial x} (x^{2} + 9 x - 4 y) = 2 x + 9

= 6 (x^{2} + 9 x - 4 y)^{5} (2 x + 9)

What is (\partial)/(\partial x)((x^2+9x-4y)^6) ?
The answer to (\partial)/(\partial x)((x^2+9x-4y)^6) is 6(x^2+9x-4y)^5(2x+9)