Tentukan turunan pertama dari fungsi $$ y=3 x^{2} \cos 6 x $$ A. $$ 6 x \cos 6 x-18 x^{2} \sin 6 x $$ B. $$ 6 x \cos 6 x+18 x^{2} \sin 6 x $$ C. $$ 6 x \cos 6 x-12 x^{2} \sin 6 x $$ D. $$ 6 x \cos 6 x+12 x^{2} \sin 6 x $$ E. $$ 3 x \cos 6 x-12 x^{2} \sin 6 x $$

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UpStudy AI · Accepted Answer

To find the derivative of 
  y = 3x² cos 6x,
we use the product rule. Let

u(x) = 3x²  and  v(x) = cos 6x.

First, compute the derivatives:
  u'(x) = 6x,
  v'(x) = –sin 6x · 6 = –6 sin 6x   (using the chain rule).

Now, applying the product rule:
  y' = u'(x)·v(x) + u(x)·v'(x)
    = 6x cos 6x + 3x² (–6 sin 6x)
    = 6x cos 6x – 18x² sin 6x.

Thus, the correct answer is option A.
The derivative of $$ y = 3x^2 \cos 6x $$ is $$ 6x \cos 6x - 18x^2 \sin 6x $$. So, the correct choice is A.

Tentukan turunan pertama dari fungsi \[ y=3 x^{2} \cos 6 x \] A. \( 6 x \cos 6 x-18 x^{2} \sin 6 x \) B. \( 6 x \cos 6 x+18 x^{2} \sin 6 x \) C. \( 6 x \cos 6 x-12 x^{2} \sin 6 x \) D. \( 6 x \cos 6 x+12 x^{2} \sin 6 x \) E. \( 3 x \cos 6 x-12 x^{2} \sin 6 x \)

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