Calculus: 1001 Practice Problems For Dummies (+ Free Online Practice). Patrick Jones
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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.
Using the Product Rule to Find Derivatives
312–331 Use the product rule to find the derivative of the given function.
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317. Find (fg)'(4) if
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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
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327. Assuming that g is a differentiable function, find an expression for the derivative of
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330. Assuming that g is a differentiable function, find an expression for the derivative of
331. Assuming that g and h are differentiable functions, find an expression for the derivative of
Using the Quotient Rule to Find Derivatives
332–351 Use the quotient rule to find the derivative.
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336. Assuming that f and g are differentiable functions, find the value of
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343. Assuming that f and g are differentiable functions, find the value of
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