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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function given is y=ln*the cubed root of 4x-1

y=ln*the cubed root of 4x-1 can be written as y = ln[(4x - 1)^(1/3)]

Use the chain rule to find y'.

y' = [1/(4x - 1)^(1/3)]*(1/3)*(4x - 1)^(-2/3)*4

=> (4/3)*1/(4x - 1)^(1/3)*(4x - 1)^(2/3)

=> (4/3)*1/(4x - 1)

The required derivative is (4/3)*1/(4x - 1)

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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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