To find the derivative of the given function, we'll apply
chain rule.
Let f(x) =
y.
We'll note the cube root as
follows:
cubed root of (4x-1) =
(4x-1)^(1/3)
We'll differentiate with respect to
x:
f'(x) = [1/(4x-1)^(1/3)]*[(1/3)*(4x-1)^(1/3 -
1)]*(4x-1)'
f'(x) =
(4/3)*(4x-1)^(-2/3)]/(4x-1)^(1/3)
f'(x) = 4/3*(4x-1)^(1/3 +
2/3)
f'(x) =
4/3*(4x-1)
The derivative of the given
function y is: f'(x) = 4/(12x - 3).
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