TERJAWAB APABILA y = (4x3 + 3) / (3x2 – 2), Maka Turunan Pertama dari Fungsi y Tersebut yang Benar Adalah y’

y’ = (12x4 + 24x2 + 18x) (3x2 – 2)2

y’ = (12x3 + 24x2 + 18x) (3x2 – 2)2

Jawaban :

To find the first derivative of the given function y = (4x^3 + 3) / (3x^2 – 2), we can use the quotient rule, which states that the derivative of (u/v) is (vdu/dx - udv/dx) / v^2.

So, let's differentiate the function step by step:

Given function: y = (4x^3 + 3) / (3x^2 – 2)

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Let u = (4x^3 + 3) and v = (3x^2 – 2)

Now, we can find the first derivative y' using the quotient rule:

y' = (v * du/dx - u * dv/dx) / v^2 = ((3x^2 - 2)(12x^2) - (4x^3 + 3)(6x)) / (3x^2 - 2)^2 = (36x^4 - 24x^2 - 24x^4 - 18x) / (3x^2 - 2)^2 = (-12x^4 - 24x^2 - 18x) / (3x^2 - 2)^2