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

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.

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

      312. math

      313. math

      314. math

      315. math

      316. math

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

      318. math

      319. math

      320. math

      321. math

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

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

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

      326. math

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

      328. math

      329. math

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

      331. Assuming that g and h are differentiable functions, find an expression for the derivative of math.

       332–351 Use the quotient rule to find the derivative.

      332. math

      333. math

      334. math

      336. Assuming that f and g are differentiable functions, find the value of math if math, math, math, and math.

      337. math

      338. math

      339. math

      340. math

      341. math

      342. math

      343. Assuming that f and g are differentiable functions, find the value of math if math, math, math, and math.

      344. math

      345. math

      346. math

      347. math

      348.


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