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

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

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

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

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

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

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

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

Simplify

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

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