Derivations

Question 1

Quotient rule differentiation y= f(x)/g(x)

Answer 1

y’ = [f’(x) . g(x) - f(x).g’(x)]/[g(x)]^2

Question 2

Product rule y= f(x).g(x)

Answer 2

y’ = f’(x).g(x) + f(x).g’(x)

Question 3

Chain rule y= [f(x)]^n

Answer 3

y’ = n.[f(x)]^(n-1) . f’(x)

Question 4

Exponential fn y=e^g(x)

Answer 4

y’ = e^g(x) . g’(x)

if any base other than e
y’ = a^g(x).g’(x).lna
a is any number

Question 5

Log fns y= ln|g(x)|

Answer 5

y’ = 1/g(x) . g’(x)

Question 6

Log fns with any other base than 10(or natural log) y=log[base a]g(x)

Answer 6

y’ = 1/[g(x).lna] .g’(x)
= g’(x)/[g(x).lna]