### Home > APCALC > Chapter 4 > Lesson 4.1.1 > Problem4-8

4-8.

For each function, write the equation of its slope function, $f ^\prime$.

1. $f\left(x\right)=\frac{2}{5}x^{-​2}-4x$

Power Rule.

2. $f(x)=-2\sqrt{x}$

Before you differentiate, rewrite $f\left(x\right)$ with a fractional exponent.

3. $f\left(x\right)=6\cos\left(x\right)$

Will $f ^\prime\left(x\right)$ be positive or negative?

4. $f ( x ) = \frac { 4 x ^ { 2 } + 4 } { x ^ { 2 } + 1 }$

Before you differentiate, factor the numerator and simplify. THINK: Will the derivative need a restricted domain? Why or why not?