Computing derivatives using the power, product, and quotient rules compute the derivative of the functions below using rules up through section 3. Find the slope, xintercept, and yintercept of the line 3x 2y 4. Before you tackle some practice problems using these rules, heres a. 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. Proofs of the product, reciprocal, and quotient rules math. Differentiate using the product and quotient rules. Ap calculus ab worksheet 26 derivatives of trigonometric functions know the following theorems examples use the quotient rule to prove the derivative of. Derivatives sum, power, product, quotient, chain rules.
In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. Quotient rule practice find the derivatives of the following rational functions. The product rule mctyproduct20091 a special rule, theproductrule, exists for di. You should discover that the results are the same and that the quotient rule is usually. 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. Ap calculus ab worksheet 22 derivatives power, package. This worksheet would work well for any class covering these derivative rules. Constant rule, constant multiple rule, power rule, sum rule, difference rule, product rule, quotient rule, and chain rule. First, treat the quotient fg as a product of f and the reciprocal of g. Worksheet for product, quotient and chain rule practicefind dydx. Progress through several types of problems that help you improve. While we do obviously have a quotient here, we also have a product in the numerator, so before we can make any progress in di. The product and quotient rules university of plymouth.
Suppose the position of an object at time t is given by ft. Use the quotient rule to find the derivative of \\displaystyle g\left x \right \frac6x22 x\. Derivative practice power, product and quotient rules. Find the first derivative of the following functions. For problems 1 6 use the product rule or the quotient rule to find the derivative of the given function. Practice worksheets for mastery of differentiation crystal clear. Although the derivatives of 1x x 1 and p x x12 are special cases of the power rule, they. P q umsa0d 4el tw i7t6h z yi0nsf mion eimtzel ec ia7ldctu 9lfues u. The following diagram gives the basic derivative rules that you may find useful. The product rule gives the formula for differentiating the product of two functions, and the quotient rule gives the formula for differentiating the quotient of two functions. Quotient rule worksheet learn the quotient rule by. Infinitely many quotient rule problems with stepbystep solutions if you make a mistake. Find a function giving the speed of the object at time t.
In this case, unlike the product rule examples, a couple of these functions will require the quotient rule in order to get the derivative. Product rule quotient rule chain rule differentiation rules with tables. 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. Others will require you to decide if a given function. S w2k0b1 q3v tkwuftwai ts jo nf4t awdakrzet 5lnlscg. There isnt much to do here other than take the derivative using the quotient rule. Scroll down the page for more examples, solutions, and derivative rules. Find the equation of the line that passes through 1.
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. L 8 gmgavdwec twxintzhh zizn yfpijnqi bt mei wcha mlsc6u cltuxsi. If you are unsure how to use the product rule to di. 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. This will be easy since the quotient fg is just the product of f and 1g. Calculus derivative rules formulas, examples, solutions. W p 4muaedlew kw wiot8h i eifn3fvi vnsittje v rcoatlhc 9u l3uts h. This worksheet is designed to be the follow up to my product and quotient rule derivatives worksheet day 1. Use proper notation and simplify your final answers. So, to prove the quotient rule, well just use the product and reciprocal rules. Power rule chain rule product and quotient rule dana ernst. State the quotient and product rule and be sure to include all necessary hypotheses. Find an equation for the tangent line to fx 3x2 3 at x 4. The product and quotient rules mathematics libretexts.
The last two however, we can avoid the quotient rule if wed like to as well see. 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 times the derivative of the first function. The product rule and the quotient rule are a dynamic duo of differentiation problems. Listofderivativerules belowisalistofallthederivativeruleswewentoverinclass. Using negative indices, differentiate by using the product rule. Lets now work an example or two with the quotient rule.
The quotient rule mctyquotient20091 a special rule, thequotientrule, exists for di. Compute the derivatives of the following functions. Free calculus worksheets created with infinite calculus. 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. Calculus i product and quotient rule practice problems. In some cases it might be advantageous to simplifyrewrite first. 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. In the last worksheet, you were shown how to find the derivative of functions like efx.