What is (\partial)/(\partial x)((5x+8y)^{11}) ?

The answer to (\partial)/(\partial x)((5x+8y)^{11}) is 55(5x+8y)^{10}

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(\partial)/(\partial x)((5x+8y)^{11})

\frac{\partial}{\partial x} ((5 x + 8 y)^{11})

55 (5 x + 8 y)^{10}

Solution steps

\frac{\partial}{\partial x} ((5 x + 8 y)^{11})

Treat

y

as a constant

Apply the chain rule:

11 (5 x + 8 y)^{10} \frac{\partial}{\partial x} (5 x + 8 y)

= 11 (5 x + 8 y)^{10} \frac{\partial}{\partial x} (5 x + 8 y)

\frac{\partial}{\partial x} (5 x + 8 y) = 5

= 11 (5 x + 8 y)^{10} \cdot 5

Simplify

= 55 (5 x + 8 y)^{10}

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

\int_{3}^{6} (2 x - 10) d x

\frac{d}{d x} (- 128 cos (2 x))

\int_{0}^{π} 7 sin^{2} (2 x) d x

\frac{d}{d x} (e^{- x} + \frac{1}{e ^{8 x}})

What is (\partial)/(\partial x)((5x+8y)^{11}) ?
The answer to (\partial)/(\partial x)((5x+8y)^{11}) is 55(5x+8y)^{10}