The product and quotient rules university of plymouth. The quotient rule in words the quotient rule says that the derivative of a quotient is the denominator times the derivative of the numerator minus the numerator times the derivative of the denominator, all divided by the square of the denominator. Power rule chain rule product and quotient rule dana ernst. The last two however, we can avoid the quotient rule if wed like to as well see. The derivative of a quotient is bottom times the derivative of the top minus the top times the derivative of the bottom, all over the bottom squared. This worksheet would work well for any class covering these derivative rules. Quotient rule practice find the derivatives of the following rational functions. Derivatives sum, power, product, quotient, chain rules. Free calculus worksheets created with infinite calculus. Find the first derivative of the following functions. Others will require you to decide if a given function.
Show by way of example that, in general, d dx f g 6 df dx dg dx and d dx f g 6 df dx dg dx. Scroll down the page for more examples, solutions, and derivative rules. For problems 1 6 use the product rule or the quotient rule to find the derivative of the given function. Use proper notation and simplify your final answers. You should discover that the results are the same and that the quotient rule is usually. There isnt much to do here other than take the derivative using the quotient rule. Quotient rule worksheet learn the quotient rule by. Constant rule, constant multiple rule, power rule, sum rule, difference rule, product rule, quotient rule, and chain rule.
This will be easy since the quotient fg is just the product of f and 1g. Although the derivatives of 1x x 1 and p x x12 are special cases of the power rule, they. Find a function giving the speed of the object at time t. If you are unsure how to use the product rule to di. The product rule and the quotient rule are a dynamic duo of differentiation problems. Ap calculus ab worksheet 22 derivatives power, package. Use the quotient rule to find the derivative of \\displaystyle g\left x \right \frac6x22 x\.
The quotient rule states that for two functions, u and v, see if you can use the product rule and the chain rule on y uv 1 to derive this formula. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. S w2k0b1 q3v tkwuftwai ts jo nf4t awdakrzet 5lnlscg. The following diagram gives the basic derivative rules that you may find useful. Find an equation for the tangent line to fx 3x2 3 at x 4. Practice worksheets for mastery of differentiation crystal clear. Find the equation of the line that passes through 1. P q umsa0d 4el tw i7t6h z yi0nsf mion eimtzel ec ia7ldctu 9lfues u. Calculus i product and quotient rule practice problems. The product and quotient rules mathematics libretexts. Practice with product and quotient rules directions. Listofderivativerules belowisalistofallthederivativeruleswewentoverinclass. In this case, unlike the product rule examples, a couple of these functions will require the quotient rule in order to get the derivative. The quotient rule mctyquotient20091 a special rule, thequotientrule, exists for di.
Theyre very useful because the product rule gives you the derivatives for the product of two functions, and the quotient rule does the same for the quotient of two functions. W p 4muaedlew kw wiot8h i eifn3fvi vnsittje v rcoatlhc 9u l3uts h. L 8 gmgavdwec twxintzhh zizn yfpijnqi bt mei wcha mlsc6u cltuxsi. First, treat the quotient fg as a product of f and the reciprocal of g. This rule is veri ed by using the product rule repeatedly see exercise203. The quotient rule is actually the product rule in disguise and is used when differentiating a fraction. Progress through several types of problems that help you improve. This worksheet is designed to be the follow up to my product and quotient rule derivatives worksheet day 1. The quotient rule is derived from the product rule and the chain rule. Some of the math problems will ask you to identify the derivative of given functions. In some cases it might be advantageous to simplifyrewrite first. Ap calculus ab worksheet 26 derivatives of trigonometric functions know the following theorems examples use the quotient rule to prove the derivative of.
Using negative indices, differentiate by using the product rule. Compute the derivatives of the following functions. In what follows we explore why this is the case, what the product and quotient rules actually say, and work to expand our repertoire of functions we can easily differentiate. Worksheet for product, quotient and chain rule practicefind dydx. The quotient rule finding the general form for the derivative for the product means we want to nd is a general form for d dx h f x hx i. Find the derivatives using quotient rule worksheets for kids. Product rule quotient rule chain rule differentiation rules with tables.
Suppose the position of an object at time t is given by ft. This time, we can use the face that division and multiplication are related to get a general rule for nding the derivative of a quotient. The product rule says that the derivative of a product of two functions is the first function times the derivative of the second function plus the second function. The product rule mctyproduct20091 a special rule, theproductrule, exists for di. Computing derivatives using the power, product, and quotient rules compute the derivative of the functions below using rules up through section 3.
Some of the worksheets below are calculus quotient rule derivative, reason for the quotient rule, the quotient rule in words, examples of the quotient rule, the quotient rule practice examples, once you find your worksheets, you can either click on the popout icon or download button to print or download your desired worksheets. The product rule is related to the quotient rule, which gives the derivative of the quotient of two functions, and the chain rule, which gives the derivative of the composite of two functions. Proofs of the product, reciprocal, and quotient rules math. Before you tackle some practice problems using these rules, heres a. Lets now work an example or two with the quotient rule. Product rule, quotient rule product rule quotient rule table of contents jj ii j i page4of10 back print version home page the derivative is obtained by taking the derivative of one factor at a time, leaving the other factors unchanged, and then summing the results.
Differentiate using the product and quotient rules. So, to prove the quotient rule, well just use the product and reciprocal rules. Find the slope, xintercept, and yintercept of the line 3x 2y 4. Infinitely many quotient rule problems with stepbystep solutions if you make a mistake. Calculus derivative rules formulas, examples, solutions.
1117 1464 22 550 441 314 769 427 1328 1098 670 387 981 680 530 451 1473 1330 1506 1510 1280 1460 915 450 963 1005 675 1139 996 469 101