What is (\partial)/(\partial x)((2x+6y)^{11}) ?

The answer to (\partial)/(\partial x)((2x+6y)^{11}) is 22(2x+6y)^{10}

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(\partial)/(\partial x)((2x+6y)^{11})

\frac{\partial}{\partial x} ((2 x + 6 y)^{11})

22 (2 x + 6 y)^{10}

Solution steps

\frac{\partial}{\partial x} ((2 x + 6 y)^{11})

Treat

y

as a constant

Apply the chain rule:

11 (2 x + 6 y)^{10} \frac{\partial}{\partial x} (2 x + 6 y)

= 11 (2 x + 6 y)^{10} \frac{\partial}{\partial x} (2 x + 6 y)

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

= 11 (2 x + 6 y)^{10} \cdot 2

Simplify

= 22 (2 x + 6 y)^{10}

\frac{11 x}{( 2 + x ^{2} )}

x \to 2 lim (\frac{x + 1}{x - 1})

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

y^{^{'}} = \frac{y ^{2}}{x ^{2}}

y = arcsin (\frac{x + 1}{x - 1})

What is (\partial)/(\partial x)((2x+6y)^{11}) ?
The answer to (\partial)/(\partial x)((2x+6y)^{11}) is 22(2x+6y)^{10}