5 Steps to a 5 AP Calculus BC 2019
82 STEP 4. Review the Knowledge You Need to Score High Example 3 Ify= ( 2 x− 1 x^2 ) 3 , find dy dx . Using the chain rule, letu ...
Differentiation 83 Example 2 Findf′(x)iff(x)=cot(4x−6). Using the chain rule, letu= 4 x−6. Then f′(x)=[−csc^2 (4x−6)][4]=−4 csc^ ...
84 STEP 4. Review the Knowledge You Need to Score High Example 8 Ify= tanx 1 +tanx , find dy dx . Using the quotient rule, letu= ...
Differentiation 85 Example 2 Findf′(x)iff(x)=tan−^1 √ x. Letu= √ x.Then f′(x)= 1 1 +( √ x)^2 du dx = 1 1 +x ( 1 2 x− (^12) ) 1 1 ...
86 STEP 4. Review the Knowledge You Need to Score High Example 1 y=e^3 x+ 5 xe^3 +e^3 dy dx =(e^3 x)(3)+ 5 e^3 + 0 = 3 e^3 x+ 5 ...
Differentiation 87 Example 8 y=ln(lnx) Letu=lnx. Then dy dx = 1 lnx du dx = 1 lnx ( 1 x ) = 1 xlnx . Example 9 y=log 5 (2x+1) Le ...
88 STEP 4. Review the Knowledge You Need to Score High Example 1 Find dy dx ify^2 − 7 y+x^2 − 4 x=10. Step 1: Differentiate each ...
Differentiation 89 Step 3: Factor out dy dx : dy dx [2(x+y)+2(x−y)− 5 y^4 ]= 5 x^4 − 2 x− 2 y+ 2 x− 2 y dy dx [2x+ 2 y+ 2 x− 2 y ...
90 STEP 4. Review the Knowledge You Need to Score High 6.4 Approximating a Derivative Given a continuous and differentiable func ...
Differentiation 91 Method 3: Using the slope of the line segment joining the points atx=2 andx=4. f(2)=2 and f(4)= 5 m= f(4)− f( ...
92 STEP 4. Review the Knowledge You Need to Score High [−2,4] by [−2,4] Figure 6.4-2 TIP • Remember that the lim x→ 0 sin 6x sin ...
Differentiation 93 Example 2 Example 1 could have been done by using implicit differentiation. Step 1: Lety=f(x), and thusy=x^3 ...
94 STEP 4. Review the Knowledge You Need to Score High TIP • You do not have to answer every question correctly to get a 5 on th ...
Differentiation 95 L’Hôpital’sRule for Indeterminate Forms Letlimrepresent one of the limits: limx→c, limx→c+, limx→c−, limx→∞,o ...
96 STEP 4. Review the Knowledge You Need to Score High Findf′(x)iff(x)=ln(3x). Answer: f′(x)= 1 3 x (3)= 1 x . Find the appro ...
Differentiation 97 6.8 Practice Problems Part A The use of a calculator is not allowed. Find the derivative of each of the follo ...
98 STEP 4. Review the Knowledge You Need to Score High 6.9 Cumulative Review Problems (Calculator) indicates that calculators ar ...
Differentiation 99 Rewritey= √ 2 x+ 1 2 x− 1 as y= ( 2 x+ 1 2 x− 1 ) 1 / 2 . Applying first the chain rule and then the quotie ...
100 STEP 4. Review the Knowledge You Need to Score High Sincef′(4) is equivalent to the slope of the tangent tof(x)atx=4, there ...
Differentiation 101 18. dy dx =(2)(sinx)+(cosx)(2x)= 2 sinx+ 2 xcosx d^2 y dx^2 =2 cosx+[(2)(cosx)+(−sinx)(2x)] =2 cosx+2 cosx− ...
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