### Home > APCALC > Chapter 8 > Lesson 8.1.4 > Problem8-43

8-43.

Differentiate. Homework Help ✎

1. $\frac { d } { d x } ( \frac { 6 x - 2 } { 3 x + 1 } )$

Quotient Rule

1. $\frac { d } { d x } [ \operatorname { sec } ( 5 \operatorname { ln } [ x ] ) ]$

$\frac{d}{dx}\sec(x)=\sec(x)\tan(x)$

1. $\frac { d } { d x } ( \frac { \operatorname { sin } ( 2 x ) } { x ^ { 3 } } )$

$=\frac{2x^{3}\text{cos}(2x)-3x^{2}\text{sin}(2x)}{x^{6}}$

1. $\frac { d } { d k } ( k ^ { 2 } 9 ^ { 3 k - 1 } )$

We know that $k$ is a variable (not a constant) because it appears in the $d/dk$.

1. $\frac { d } { d x } [ \operatorname { sin } ^ { 2 } ( x ) \operatorname { cos } ( x ) ]$

Product Rule