### Home > APCALC > Chapter 5 > Lesson 5.2.1 > Problem5-52

5-52.

Differentiate each function if possible. If the function is one you cannot differentiate yet, say so and explain how you know. Be sure to use the appropriate notation.

You have the skills to find the derivative of five out of six of the problems below.

1. $y=x^{100}+100x$

Power Rule.

2. $H(t)=t^{-4}−6\sqrt{x}$

Before differentiating, rewrite the square root with a fractional exponent.

3. $y = x · 2^x$

Do you know how to find a derivative of $2^{x}$?

4. $y = x^8 \operatorname{cos}(x)$

Use the Product Rule.

5. $f (x) = x^5(x^3 + π)$

Distribute first. Or use the Product Rule.

6. $y = \large\frac { 7 } { x } - \frac { x } { 7 }$

Before differentiating, rewrite the first fraction with exponents.