Question

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

full method​

Answer 1

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)^{(1)/(3)}\\\\(dy)/(du) = (1)/(3)(2u^2 + 3)^(-2)/(3)(4u)\\\\(dy)/(du) = (4u)/(3)(2u^2 + 3)^(-2)/(3)\\\\(dy)/(du) = (4u)/(3(2u^2 + 3)^(2)/(3))`

and for the second one:

`u = √(2x + 1)\\\\u = (2x + 1)^(0.5)\\\\(du)/(dx) = 0.5(2x + 1)^(-0.5)(2)\\\\(du)/(dx) = (1)/(√(2x + 1))`