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Question 1

how do you find dy/dx implicit differentiation

Answer 1

whatever exponent is on the top, replace with dy/dx
find the derivative
solve for dy/dx

Question 2

Find dy or dx /dt given the opposite and a point

Answer 2

find the derivative and multiply by d/dt
solve for the thing you’re trying to solve for
plug in numbers

Question 3

volume of a sphere problems

Answer 3

find the derivative of volume and multiply it by dr/dt
plug in known values

Question 4

chain rule

Answer 4

derivative of outside of function (leave inside alone) * derivative of inside of function

Question 5

when do you use the chain rule?

Answer 5

when you have a function inside and something outside
ex. sin 3x-> yes
sinx-> no

Question 6

when do you use the chain rule more than once?

Answer 6

when you use the chain rule and there are 2 or more functions left, usually with more than x

Question 7

chain rule with a square root

Answer 7

convert to an exponent
rewrite as 1/2√(x)^-1/2 x’
write as y= x’/2√x
ex. √3x^2 -> 6x/2√3x^2+1

Question 8

How do you find a derivative when given a rule and a list of values

Answer 8

Identify the rule
Plug in the given numbers for the regular and derivative as necessary
Simplify

Question 9

implicit differentiation

Answer 9

take the derivative of both sides for x
x is regular derivative
multiply y by dy/dx
solve for dy/dx

Question 10

do you have to use the product rule?

Answer 10

YESSSSSSSSSSSS

Question 11

2nd implicit differentiation

Answer 11

take the derivative again
take y out and find the derivative + multiply by dy/dx
plug back in * multiply by dy/dx
plug in original dy/dx

Question 12

d/dx sin⁻¹

Answer 12

1/√1-x²

Question 13

d/dx tan⁻¹

Answer 13

1/x²+1

Question 14

d/dx sec⁻¹

Answer 14

1/|x|*√x²-1

Question 15

d/dx cos⁻¹

Answer 15

-1/√1-x²

Question 16

d/dx cot⁻¹

Answer 16

-1/x²+1

Question 17

d/dx csc⁻¹

Answer 17

-1/|x|√x²-1

Question 18

d/dx e^x

Answer 18

e^x

Question 19

d/dx A^x

Answer 19

A^x * lnA

Question 20

d/dx |x|

Answer 20

x/|x|

Question 21

d/dx lnx

Answer 21

1/x

Question 22

d/dx logAx

Answer 22

1/x*lnA