||
Membaca
SIMAK UI 2010

Solusi SIMAK UI 2010 Kode 509 [IPA] – Nomor 10


Diketahui\ f\ adalah\ fungsi\ di\ mana
f'(x)=\frac{1}{x^2+1}
Jika\ g(x)=f(3x-1),\ maka\ g'(x)=....
(A)\quad \frac{1}{(3x-1)^2+1}
(B)\quad \frac{3}{(3x-1)^2+1}
(C)\quad \frac{3}{(3x-1)^2}
(D)\quad \frac{1}{(3x-1)^2}
(E)\quad \frac{-3}{(3x-1)^2+1}
Jawaban: A

Misalkan\ x=tan\ t
maka

\begin{array}{rcl} t & = & arc\ tan\ x \\ dx & = & sec^{2}t\ dt \\ x^2+1 & = & tan^{2}t+1 \\ & = & sec^{2}t \end{array}
sehingga

\begin{array} {lcl} f(x)&=&\int \frac{1}{x^2+1}\ dx\\\\&=&\int \frac{sec^{2}t}{sec^{2}t}\ dt\\\\&=&\int dt\\\\&=&t\\\\&=&arc\ tan\ x\end{array}

f'(x)=\frac{1}{x^2+1}\quad \leftrightarrow \quad f(x)=arc\ tan\ x

Karena\ g(x)=f(3x-1)\ maka\ g(x)=arc\ tan\ (3x-1)
sehingga

g'(x)=\frac{1}{(3x-1)^2+1}

About Kalakay

Guru Matematika SMK

Diskusi

Belum ada komentar.

Tinggalkan Balasan

Isikan data di bawah atau klik salah satu ikon untuk log in:

Logo WordPress.com

You are commenting using your WordPress.com account. Logout / Ubah )

Gambar Twitter

You are commenting using your Twitter account. Logout / Ubah )

Foto Facebook

You are commenting using your Facebook account. Logout / Ubah )

Foto Google+

You are commenting using your Google+ account. Logout / Ubah )

Connecting to %s

%d blogger menyukai ini: