Limits and Derivatives

Limits and Derivatives

Question

Find the derivatives of the following :

(ax+b)(cx+ d)

Answer

Let         y  =     (ax+b)(cx+ d)
differentiating both  sides  w.r.t.   x,   we  get
space space space space space space space space space dy over dx equals straight d over dx left square bracket left parenthesis ax plus straight b right parenthesis to the power of straight n space left parenthesis cx plus space straight d right parenthesis to the power of straight n right square bracket
  space space space space space space space space space space space space space space space space space equals space space space space left parenthesis ax space plus straight b right parenthesis to the power of straight n straight n left parenthesis cx plus straight d right parenthesis to the power of straight n minus 1 space end exponent straight c space plus space left parenthesis cx plus straight d right parenthesis to the power of straight n space straight d over dx left parenthesis ax plus straight b right parenthesis to the power of straight n
      space space space space space space space equals space space space space left parenthesis ax plus straight b right parenthesis to the power of straight n straight n left parenthesis cx plus straight d right parenthesis to the power of straight n minus 1 end exponent straight c plus left parenthesis cx plus straight d right parenthesis to the power of straight n space straight n space left parenthesis ax plus straight b right parenthesis to the power of straight n minus 1 end exponent a
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      space space space space space space space space space space space space equals space straight n open parentheses ax plus straight b close parentheses to the power of straight n minus 1 end exponent open parentheses cx plus straight d close parentheses to the power of straight n minus 1 end exponent open parentheses 2 ax plus bc plus ad close parentheses

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