Jika $$ f(x)= an \left(3 x^{2}+8 ight) $$ maka nilai dari $$ f^{\prime}(x)= $$. A. $$ 6 \operatorname{Sec}^{2}\left(3 x^{2}+8 ight) $$ B. $$ 3 \sec ^{2}\left(3 x^{2}+8 ight) $$ C. $$ 3 x \sec ^{2}\left(3 x^{2}+8 ight) $$ D. $$ 3 x an ^{2}\left(3 x^{2}+8 ight) $$ E. $$ \quad 6 x \sec ^{2}\left(3 x^{2}+8 ight) $$

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Jika $$ f(x)=	an \left(3 x^{2}+8ight) $$ maka nilai dari $$ f^{\prime}(x)= $$. A. $$ 6 \operatorname{Sec}^{2}\left(3 x^{2}+8ight) $$ B. $$ 3 \sec ^{2}\left(3 x^{2}+8ight) $$ C. $$ 3 x \sec ^{2}\left(3 x^{2}+8ight) $$ D. $$ 3 x 	an ^{2}\left(3 x^{2}+8ight) $$ E. $$ \quad 6 x \sec ^{2}\left(3 x^{2}+8ight) $$

UpStudy AI · Accepted Answer

Untuk mencari turunan dari fungsi $$ f(x) = \tan(3x^2 + 8) $$, kita akan menggunakan aturan rantai.

1. Pertama, kita ingat bahwa turunan dari $$ \tan(u) $$ adalah $$ \sec^2(u) \cdot u' $$, di mana $$ u = 3x^2 + 8 $$.
2. Maka, kita perlu menghitung $$ u' $$:
   $$
   u = 3x^2 + 8 \implies u' = \frac{d}{dx}(3x^2 + 8) = 6x
   $$

3. Sekarang kita dapat menghitung $$ f'(x) $$:
   $$
   f'(x) = \sec^2(3x^2 + 8) \cdot u' = \sec^2(3x^2 + 8) \cdot 6x
   $$

Jadi, kita mendapatkan:
$$
f'(x) = 6x \sec^2(3x^2 + 8)
$$

Dengan demikian, jawaban yang benar adalah:
**E. $$ 6 x \sec^{2}(3 x^{2}+8) $$**.
$$ f^{\prime}(x) = 6 x \sec^{2}(3 x^{2}+8) $$ Therefore, the correct answer is E. $$ 6 x \sec^{2}(3 x^{2}+8) $$.

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