Week 2 Differentiation

Question 1

give the first principle of differentiation equation

Answer 1

dy/dx = lim𝛿x–>0 [f(x+𝛿x)-f(x)] / 𝛿x

Question 2

what is the product rule for differentiation

Answer 2

when you have
y = uv
then
y’ = uv’ + u’v

Question 3

what is the chain rule for differentiation

Answer 3

when you have
y = u(x)
then
dy/dx = dy/du x dy/dx

Question 4

what is the quotient rule for differentiation

Answer 4

when you have
y = u/v
then
y’ = [u’v - uv’] / v^2

Question 5

what is the implicit differentiation rule

Answer 5

when you have
d/dx [f(y)]
then this is =
df/dy x dy/dx

Question 6

what is the parametric differentiation rule

Answer 6

dy/dx = dy/dt x (dx/dt)^-1

Question 7

what is the general notation for differentiation

Answer 7

d^nf/dx^n = f^n(x)

Question 8

how do we represent that a function has been differentiated wrt time

Answer 8

put dots above it. one dot per derivative

Question 9

what musta function be to be differentiated

Answer 9

must be continuous

Question 10

what is the derivative of tanx

Answer 10

sec^2(x)

Question 11

what is the derivative of lnx

Answer 11

1/x

Question 12

what is the derivative of ln[g(x)]

Answer 12

g’(x) / g(x)

Question 13

what is the derivative of sinh(x)

Answer 13

cosh(x)

Question 14

what is the derivative of cosh(x)

Answer 14

sinh(x)

Question 15

what is the logarithmic differentiation equation

Answer 15

dln[f(x)]/dx = f'(x) / f(x)
dln(y)/dx = 1/y x dy/dx

Question 16

what is the inverse function differentiation rule

Answer 16

dx/dy = (dy/dx)^-1

Question 17

what is the small changes rule for differentiation

Answer 17

if a derivation is used to estimate a small change in one quantity that depends on another then we can say that
f’(x) ≈ 𝛿y/𝛿x => 𝛿y ≈ f’(x)𝛿x