Do I have these derivative rules correct?

Question

I havn't done these in a while and want to make sure I still know what im talking about.

1) (k^b)' = (k^b) (b ') (ln k)
    ex: (3^ 2x)' = (3 ^ 2x) (2) (ln 3)
         (2e^ 5x)' = (2) ( e ^ 5x) (5) (ln e) + ( 0 ) (e^5x)
                      = 10e^5x  
2) ( log base k (b)) ' = (1/ b ln (k)) (b')
      ex: (log base 3 (7x))' = (1/ 7x ln 3) (7)
           (log base e (x/9)  = (1/ (x/9) ln (e)) [ ((9) (1) - (0) (x)) / 9^2]
                                    = (1/ (x/9) (1)) (9/81)
                                    = (9/x) (1/9)
                                    = 1/x
Sorry I know that its alot of math to follow i just want to make sure that I have the theory right.

nudnik0 · Accepted Answer

Yes, these are correct.  Also, you can reduce your workload when differentiating C f(x) by using the rule

(d/dx)(C f(x)) = C df/dx 
(C a constant)

rather than the more general rules

(d/dx)(f(x) g(x)) = df/dx g(x) + f(x) dg/dx,
(d/dx)(f(x) / g(x)) = (df/dx g(x) - f(x) dg/dx)/g(x)^2.

Trending News

Do I have these derivative rules correct?

1 Answer