Derivative Formulas

Question 1

Product Rule

Answer 1

derivative of the 2nd function first
f(x)g’(x) + f’(x)g(x)

Question 2

Quotient Rule

Answer 2

derivative of the numerator first
f’(x)g(x) - f(x)g’(x) / g(x)^2

Question 3

derivative of tan(u)

Answer 3

sec^2(u) u’

Question 4

derivative of sec(u)

Answer 4

sec(u)tan(u)u’

Question 5

derivative of csc(u)

Answer 5

-csc(u)cot(u)u’

Question 6

derivative of cot(u)

Answer 6

-csc^2(u)u’

Question 7

derivative of ln(u)

Answer 7

u’/u

Question 8

derivative of e^u

Answer 8

u’e^u

Question 9

derivative of a^u

Answer 9

u’(a^u)(ln a)

Question 10

derivative of arcsin(u)

Answer 10

u’/(1 - u^2)^1/2

Question 11

derivative arccos(u)

Answer 11

-u’/(1 - u^2)^1/2

Question 12

derivative of arctan(u)

Answer 12

u’/1 + u^2

Question 13

derivative of arccot(u)

Answer 13

-u’/1 + u^2

Question 14

derivative of arcsec(u)

Answer 14

u’/(u^2 -1)^1/2*(abs u)

Question 15

derivative of arccsc(u)

Answer 15

u’/(u^2 - 1)^1/2*(abs u)

Question 16

How to take derivative of an absolute value function?

Answer 16

1. The Abs funct can’t be diff. where f(x) = 0 (or where it turns) so split it up at that point
2. d/dx abs.f(x) = f’(x) at x > pt.
   -f’(x) at x < pt.
   undef at x = pt.
3. So use that piecewise function to find whatever value you need to, the function will have a ‘cusp’ at x = the turning point!