# Derivative Practice – Numbers

Here is an example of how to help your students practice their derivative rules in a different way.  Tomorrow another different approach.
Let f be a differentiable function. The table below gives values of f and g their first derivatives at selected values of x

 x -2 0 2 4 6 $f\left( x \right)$ -8 0 –2 2 5 ${f}'\left( x \right)$ 2 4 –3 –1 0 $g\left( x \right)$ 2 4 5 6 5 ${g}'\left( x \right)$ 1 2 4 3 2
1. If $h\left( x \right)=f\left( x \right)+3g\left( x \right)$ find  ${h}'\left( 2 \right)$
2. If $\displaystyle j\left( x \right)=\frac{f\left( x \right)}{g\left( x \right)}$ find  ${j}'\left( 4 \right)$
3. If  $r\left( x \right)=f\left( g\left( x \right) \right)$  find  ${r}'\left( 0 \right)$
4. If  $s\left( x \right)=g\left( f\left( x \right) \right)$  find  ${s}'\left( 2 \right)$
5. If  $q\left( x \right)=g\left( x \right)f\left( x \right)$ find  ${q}'\left( -2 \right)$
6. Approximate  ${g}'\left( 3 \right)$
7. Write an equation of the line tangent to g at the at the point where = 0.

Answers:

1. 9,     2. -1/3,     3. -2,     4. -3,     5. -5,     6. 1/2,    7.  y=4+2(x-0) or y = 4+2

## 4 thoughts on “Derivative Practice – Numbers”

1. How can you find the tangent to g at the origin, when it doesn’t go through the origin?

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2. Hi. Can you help me with #5? How is it q(x)? I’m confused. Thanks.

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• My mistake. Thanks for catching this. I have corrected the answer to #5

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