What-is-derivative-for-this-function-a-b-x-1-c-1-2-x-1-x-2-d-1-6-x-1-x-2-x-3-

Question Number 72823 by Raxreedoroid last updated on 03/Nov/19

What is derivative for this function

a \times b^{x - 1} \times c^{\frac{1}{2} (x - 1) (x - 2)} \times d^{\frac{1}{6} (x - 1) (x - 2) (x - 3)}

Answered by mind is power last updated on 03/Nov/19

f (x) = b^{x - 1} c^{\frac{(x - 1) (x - 2)}{2}} . d^{\frac{(x - 1) (x - 2) (x - 3)}{6}}

\ln (f (x)) = (x - 1) \ln (b) + \frac{(x - 1) (x - 2)}{2} \ln (c) + \frac{(x - 1) (x - 2) (x - 3)}{6} \ln (d)

\Rightarrow \frac{f^{'}}{f} = \ln (b) + \frac{(2 x - 3)}{2} \ln (c) + (\frac{{3 x}^{2} - 12 x + 11}{6}) \ln (d)

\Rightarrow \frac{f^{'}}{f} = \ln ({bc}^{\frac{2 x - 3}{2}} d^{\frac{{3 x}^{2} - 12 x + 11}{6}})

\Rightarrow f^{'} = {ab}^{\frac{x - 1}{}} . c^{\frac{(x - 1) (x - 2)}{2}} . d^{\frac{(x - 1) (x - 2) (x - 3)}{6}} . \ln (b . c^{\frac{2 x - 3}{2}} . d^{\frac{{3 x}^{2} - 12 x + 11}{6}})