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

The answer to (\partial)/(\partial x)((9x+2y)^6) is 54(9x+2y)^5

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

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

54 (9 x + 2 y)^{5}

Solution steps

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

Treat

y

as a constant

Apply the chain rule:

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

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

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

= 6 (9 x + 2 y)^{5} \cdot 9

Simplify

= 54 (9 x + 2 y)^{5}

x \to 0 lim (x^{4} cos (\frac{3}{x}))

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

\frac{d}{d t} (sinh (t))

e^{4 t} (5 t^{4} + 9 t^{3} + 11 t)

y = \frac{1}{x ^{2}}, (1, 1)

What is (\partial)/(\partial x)((9x+2y)^6) ?
The answer to (\partial)/(\partial x)((9x+2y)^6) is 54(9x+2y)^5