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f(x) =x(x-1)(x-2)...(x-10)
ln(f(x)) = lnx +ln(x-1)+...+ln(x-10)
f'(x)/f(x) = [ 1/x -1/(x-1) +...+1/(x-10) ]
f'(x) = [ 1/x -1/(x-1) +...+1/(x-10) ] .x(x-1)(x-2)...(x-10)
f'(5)
=5(5-1)(5-2)(5-3)(5-4)(5-6)(5-7)(5-8)(5-9)(5-10)
=5(4)(3)(2)(1)(-1)(-2)(-3)(-4)(-5)
=-14400
ln(f(x)) = lnx +ln(x-1)+...+ln(x-10)
f'(x)/f(x) = [ 1/x -1/(x-1) +...+1/(x-10) ]
f'(x) = [ 1/x -1/(x-1) +...+1/(x-10) ] .x(x-1)(x-2)...(x-10)
f'(5)
=5(5-1)(5-2)(5-3)(5-4)(5-6)(5-7)(5-8)(5-9)(5-10)
=5(4)(3)(2)(1)(-1)(-2)(-3)(-4)(-5)
=-14400
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