Write The Composite Function In The Form F(g(x)). [identify The Inner Function U = G(x) And The Outer Function Y = F(u).]

`y = root(3)(1 + 4x)` Write the composite function in the form f(g(x)). Identify the inner function u = g(x) and the outer function y =f(u). Then find the derivative dy/

Expert Answers

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Note:- 1) if y = x^n ; then dy/dx = n*x^(n-1)

Thus,

If y = (1+4x)^(1/3) ; then 

Let f(x) = x^(1/3)...........(1)

And g(x) = (1+4x).........(2)

Thus, f(g(x)) = (1+4x)^(1/3)  .................Answer

Now, dy/dx = y' = (1/3)*{(1 + 4x)^(-2/3)}*4

or, dy/dx = (4/3)*[(1+4x)^(-2/3)]

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