Differentiation Questions and Answers

How can you 115 DISCUSS Equations That Are Not Identities tell if an equation is not an identity Show that the follow ing equations are not identities a sin 2x 2 sin x b sin x y sin x sin y c sec x csc x 1 1 sin x cos X d csc x sec x

71 72 73 1 sec x tan x cos t tan t 1 sin t 1 sin x 1 sin x sec x tan x tan t 1 sin x 1 sin x 2 sec x 4 tan x sec x

Find the equation of the tangent line at the given poin 4 2 5 x y 3 at 1 2 2 2x 2 6 y e 3y x at 0 3

3 If 2x 3y 5xy then use implicit differentiation to find dy dr

4 If x y 6x y 8 0 then use implicit differentiation to find dx 1 1 6

Q16 Find for y 9x xe ex a 9 ex log 9 x e 9x ex b 9 exe 1 log9 x e 9x8x c 9 x log 9 x e9 9x e d 9 ex log 9 re 9x ex

A company that produces cell phones has a cost function of C 19x 136x 6414 where C is the cost in dollars and is the number of cell phones produced in thousands How many units of cell phone in thousands minimizes the cost function x thousand phones produced will minimize C

dy 7 Compute and simplify for y x x dx

Find the derivative of Type all the steps that you took to find your answer and show all the steps f 1 tan 1 8 1

6 Determine the equation of the tangent line for sin x y 2x at the point 0 7 Write your answer in y mx b 7 Compute and simplify dy for y x x x

First explain in English how you would find the derivative of the given function and list all differentiation rules that you can or need to use to find the derivative Then find its derivative x tan x f x

d dx 347 24 8 XY dx xy 2xy Y xy 2y yy 2y 2xy 2x y dx JA 2 2xy dx y 2y yy 4xy2y 2x 2xyy yy 2x y 2xy xy 2y 27 X y 2x 2xy 4x 2y 24 xy dy x y 2 y 2 ry Y xy xy jz X2x y XX 2 1 2XX X XY y 2 x 2 y xy 2714y 2y 2xy xy 2 dy y 4x4 2y 2y Y 2x 2xy 4 If A x and h denote the area length of a side and altitude of an equilateral triangle respectively then they are related by the formulas A x and x 2 3 h Determine the rate of change of the area with respect to the altitude and determine the rate of change when h 3 3

mr warren the physical education teacher has 7 boes of helmet each box has h helmets write an expression to represent the total number of helmets

Are there any errors in this example There are no errors up to this point in the solution There is an error in the solution d7x6 d dx dx dx 1 2 d dx 7x4

stimate the instantaneous rate of change of the function f x x 4x 3 at x mange over successively smaller intervals elect the correct answer below D 13 12 11 O 10 9 0 7 3 using the average rate c

If f x 3x sin 2 find f 0 7 Note Don t try to use sin r in your answe

Find the derivative of the function f u f u U u 5 2u 5 5 2 X

4 0 1 Points Find the derivat f t

If the lake level drops 0 038 metres it drops mm

Consider the following P x x 4x 15x Use the remainder theorem to determ x 4 is a zero of P x 1 is a zero of P

YouTube SISD EPCC 1 1 Points DETAILS f x Paraphrasing Tool Find the value of the derivative if it exists at the indicated x 7 LARCALC12 3 1 007 y 2 1

1 Metric System A company used 8 g Ounces o

Consider the function f x x near x 8 Find the linear approximation error when using the linear approximation to estimate 7 85 O 0 00008 O 0 00008 1 9875

Metric System One meter is about 3 a the equivalent of c b the equivalent of c

Choose the correct answer b 225 cm 225 km 225 mm

Make an approximate d 203 lb to kilograms 203 lb kg

Metric System Convert the given quantity to 24 6 ml to fluid ounces

Indicate the metric unit of measure Choose the correct answer below Square kilometers Cubic kilometers Square millimeters Cubic millimeters

priate Ted is driving near Rome and sees Choose the correct answer below 6 cm 6 km

2 a Set up the following integral in spherical coordinates compute it iiint R frac z left x 2 y 2 z 2 right frac 3 2 d V where R is the region in the first octant defined by with x y x 9 3 2 2 Set up the above integral in cylindrical coordinates but do not compute it b Find the volume of the solid bounded by 2 y 5x z z y 2x

ntered Answer Preview t 2 x 8t x

PREVIEW ONLY ANS Problem 9 1 point Give exact answers no de

1 point Match the functions and their deriv 1 y tan x 2 y sin x tan x 3 y cos x 4 y cos tan x A y 3 cos x tan x B y sin tan x cos x C y 1 tan x D y sin x tan x sec x Note You can earn partial credit on this prob

1 f x cos x 4 2 f 5 ote You can earn part

4 Given f x 2 ln x tan x find f x

Use the limit definition to find the derivative of f x x

5 Given g x 5x 1 3x 1 3 find and simplify g x

Replace the question m 6 cm m 6 cm m Simplify your answe

Anne Frank s family left Germany in order 0 Join the war effort Return to their homeland Escape discrimination

How many triangles can be forme m B 127 a 33 b 4 O No Triangles O One Triangle

Fill in the blank to complete the trigonometric formula 1 cos 2u 1 cos 2u 11

Should you use the Law of Sines or La 14 in 117

and Sigma Notation Which answer represents the series in sigma notation 5 1 3 7 11

a Find the following side lengths for the net A 3cm B 10cm C 8cm D 6cm b Use the net to find the surface area of the prism cm 2

Find the function y y x given dy dx x 7 e y y 7 ln 7 B

Find y and then find the slope of the tangent line at 2 0 0016 y 5x 15 y 2 x 3 3 2 25 The tangent line at 2 0 0016 is y x Enter an integer or decimal number more V

If f x 2x sin r then f x f 0 3 Note Don t try to use sin x in your answers use arcsin x instead Round to the nearest hundredth

en find the slope of the tangent line a ne at 192 48 is 3

dy If y sin 5x then dz A B C D E 1 1 2522 5 1 25x 5 1 2522 1 1 25x 5 1 25x

If 4y and if y 4 when x 0 then y A B C D 464x 4e ext 3 e4x