What is (\partial)/(\partial x)((2-sqrt(x))^6) ?

The answer to (\partial)/(\partial x)((2-sqrt(x))^6) is -(3(-sqrt(x)+2)^5)/(sqrt(x))

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(\partial)/(\partial x)((2-sqrt(x))^6)

\frac{\partial}{\partial x} ((2 - x)^{6})

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

Solution steps

\frac{\partial}{\partial x} ((2 - x)^{6})

Apply the chain rule:

6 (2 - x)^{5} \frac{\partial}{\partial x} (2 - x)

= 6 (2 - x)^{5} \frac{\partial}{\partial x} (2 - x)

\frac{\partial}{\partial x} (2 - x) = - \frac{1}{2 x}

= 6 (2 - x)^{5} (- \frac{1}{2 x})

Simplify

6 (2 - x)^{5} (- \frac{1}{2 x}) : - \frac{3 ( - x + 2 ) ^{5}}{x}

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

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What is (\partial)/(\partial x)((2-sqrt(x))^6) ?
The answer to (\partial)/(\partial x)((2-sqrt(x))^6) is -(3(-sqrt(x)+2)^5)/(sqrt(x))