Derivatives

Question 0

The Product Rule

Answer 0

1Dx2+2Dx1

Question 1

Derivative by definition formula

Answer 1

f(x)=limit f(x+h)-f(x)/h
h->0

Step 1: every (x) gets replaced by (x+h)
Step 2: subtract original function
Step 3: divide by h
Step 4: plug in 0 for h

Question 2

The Quotient Rule

Answer 2

LoDxHi-HiDxLo/LoLo

Question 3

The Chain Rule

Answer 3

Dx of outside…don’t change the inside…times the Dx of inside

Question 4

Trig Rule

Answer 4

Dxtrig times the box…Dx of box

Question 5

e^x

Answer 5

e to the box times the Dx of box

Question 6

Y=ln◽️

Answer 6

1/◽️ times Dx◽️

Question 7

Tangent Line at given point

Answer 7

Derivative…plug in x-value….point-slope form

Question 8

Normal line to the function at given point

Answer 8

Derivative…plug in x-value…-(reciprocal)…point-slope form

Question 9

Absolute extrema

Answer 9

[closed points]
Derivative…set equal to zero for critical points…plug critical points and end values[ ] into original equation…see greatest and least for max and min

Question 10

Ln(ab)

Answer 10

lna+lab

Question 11

Ln(a/b)

Answer 11

lna-lnb

Question 12

Lna^b

Answer 12

blna