Diketahui f(x)=(3x+5)/(x+4) , maka f'(x)=

Diketahui $f(x)=\frac{3x+5}{x+4}$, maka $f^{\prime }(x)=\dots$

A. $\frac{17}{(x+4{)}^2}$

B. $\frac{6x}{(x+4{)}^2}$

C. $\frac{7}{(x+4{)}^2}$

D. $-\frac{6x}{(x+4{)}^2}$

E. $-\frac{7}{(x+4{)}^2}$

Jawab

diketahui:$f(x)=\frac{3x+5}{x+4}$

ditanya:$f^{\prime }(x)=$

Jawab

misal: $u=3x+5\to u^{\prime }=3$

$v=x+4\to v^{\prime }=1$

$\frac{u^{\prime }v-u{v}^{\prime }}{v^2}$

$=\frac{3(x+4)-(3x+5)}{(x+4{)}^2}$

$=\frac{3x+12-3x+5}{(x+4{)}^2}$

$=\frac{7}{(x+4{)}^2}$

jawaban: C

Muda Berkarya Intelektual Normatif

Muda Berkarya Intelektual Normatif