Mathematics: Use the chain rule to calculate y = (2u² + 3)⅓ and u = √(2x +1)full method

A 14/60 or 7/30B 12/60=x/300 X=60...

Use the chain rule to calculate y = (2u² + 3)⅓ and

Ответ:

lexiemornelas

17.03.2022

Given the reference to the chain rule, I assuming by "calculate", you mean "take the derivative of", in which case we have:

For the first function:

$y = (2u^2 + 3)^{\frac{1}{3}}\\\\\frac{dy}{du} = \frac{1}{3}(2u^2 + 3)^\frac{-2}{3}(4u)\\\\\frac{dy}{du} = \frac{4u}{3}(2u^2 + 3)^\frac{-2}{3}\\\\\frac{dy}{du} = \frac{4u}{3(2u^2 + 3)^\frac{2}{3}}$

and for the second one:

$u = \sqrt{2x + 1}\\\\u = (2x + 1)^{0.5}\\\\\frac{du}{dx} = 0.5(2x + 1)^{-0.5}(2)\\\\\frac{du}{dx} = \frac{1}{\sqrt{2x + 1}}$

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Use the chain rule to calculate y = (2u² + 3)⅓ and u = √(2x +1)

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