Patrick Jones - Calculus - 1001 Practice Problems For Dummies (+ Free Online Practice)

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310–311Find all points on the given function where the slope of the tangent line equals the indicated value.

310. Find all x values where the function has a horizontal tangent line.

311. Find all x values where the function has a tangent line with a slope equal to 6.

Chapter 5

This chapter focuses on some of the major techniques needed to find the derivative: the product rule, the quotient rule, and the chain rule. By using these rules along with the power rule and some basic formulas (see Chapter 4), you can find the derivatives of most of the single-variable functions you encounter in calculus. However, after using the derivative rules, you often need many algebra steps to simplify the function so that it’s in a nice final form, especially on problems involving the product rule or quotient rule.

Here you practice using most of the techniques needed to find derivatives (besides the power rule):

The product rule

The quotient rule

The chain rule

Derivatives involving trigonometric functions

Many of these problems require one calculus step and then many steps of algebraic simplification to get to the final answer. Remember the following tips as you work through the problems:

Considering simplifying a function before taking the derivative. Simplifying before taking the derivative is almost always easier than finding the derivative and then simplifying.

Some problems have functions without specified formulas in the questions; don’t be thrown off! Simply proceed as you normally would on a similar example.

Many people make the mistake of using the product rule when they should be using the chain rule. Stop and examine the function before jumping in and taking the derivative. Make sure you recognize whether the question involves a product or a composition (in which case you must use the chain rule).

Rewriting the function by adding parentheses or brackets may be helpful, especially on problems that involve using the chain rule multiple times.

312–331Use the product rule to find the derivative of the given function.

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317. Find ( fg )'(4) if , , , and .

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323. Assuming that g is a differentiable function, find an expression for the derivative of .

324. Assuming that g is a differentiable function, find an expression for the derivative of .

325. Find ( fg )'(3) if , , , and .

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