derivative rules

Question 1

constant functions

Answer 1

if there’s no variable and the number isnt beside sin or cos etc its zero

Question 2

power rule 1

Answer 2

what ever the exponent is bring it in front of the variable and multiple the variable then subtract 1 form the original exponent leaving a new exponent that is one less

Question 3

quotient rule

Answer 3

use this when given fractions
formula: g x f’ - f x g’ / g^2

remember to distribute the negative first then collect like terms

Question 4

constant multiple rule

Answer 4

use this when a constant is multiplying by a variable just get the derivative of the variable multiplied by the constant don’t take the derivative of the constant

formula c x f(x) c x d/dx f(x)

Question 5

product rule

Answer 5

use when multiplying functions ( if the functions are being added then its not product rule)
formula: (fxg) = f’ x g + f x g’
three functions f’ x g x h + f x g’ x h + f x g x h’

just rember that we only do this for multiplication and when we see addition we just group up the functions

Question 6

chain rule

Answer 6

basically just get the derivative of the function that is surrounding everything then work inwards and keep on getting the derivatives of the functions until there are non left. remember that every time you take the derivative then you cant use that one anymore

formula f o g = f’ (g(x)) x g’