Thursday, October 1, 2015

Find the derivative of y=ln*the cubed root of 4x-1

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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