Question

#Math Challange Diferensial

Carilah turunan dari fungsi :

Answer 1

Subtitusi : a = x²-6x+1, b = cos(a²), c = sin(b), d = tan(c), e = sin(d)

e = sin(tan(sin(cos((x²-6x+1)²))))

f(x) = sin(e)

f'(x) = cos(e).d(e)

     = cos(e).d(sin(d))

   =  cos(e).cos(d).d(d)

   = cos(e).cos(d).d(tan(c))

   = cos(e).cos(d).sec²(c).d(c)

   = cos(e).cos(d).sec²(c).d(sin(b))

   = cos(e).cos(d).sec²(c).cos(b).d(b)

   = cos(e).cos(d).sec²(c).cos(b).d(cos(a²))

    = -cos(e).cos(d).sec²(c).cos(b).sin(a²).d(a²)

   = -2cos(e).cos(d).sec²(c).cos(b).sin(a).a.d(a)

   = -2cos(e).cos(d).sec²(c).cos(b).sin(a).a.d(x²-6x+1)

 = -2a.cos(e).cos(d).sec²(c).cos(b).sin(a).(2x-6).dx

f'(x) = -4a.cos(e).cos(d).sec²(c).cos(b).sin(a).(x-3)

       = -a.sec²(c).(x-3).(2.cos(d).cos(e).2.sin(a).cos(b))

      = -a.sec²(c).(x-3).((cos(d+e)+cos(d-e)).(sin(a+b)+sin(a-b))

      = -a.sec²(c).(x-3).(cos(d+e).sin(a+b)+cos(d+e).sin(a-b)+cos(d-e).sin(a+b)+cos(d-e).sin(a-b))

      = -a.sec²(c).(x-3).(1/2.(sin(a+b+d+e) + sin(a+b-d-e))+1/2 . (sin(a-b+d+e)+sin(a-b-d-e))+1/2.(sin(a+b+d-e)+sin(a+b-d+e))+1/2.(sin(a-b+d-e)+sin(a-b-d+e)) )

    = -1/2 . a . sec²(c).(x-3).(sin(a+b+d+e)+sin(a+b-d-e)+sin(a-b+d+e)+sin(a-b-d-e)+sin(a+b+d-e)+sin(a+b-d+e)+sin(a-b+d-e)+sin(a-b-d+e))

    = -1/2 . (x²-6x+1).sec²(sin(cos((x²-6x+1)²))).(x-3).(sin((x²-6x+1)+(cos((x²-6x+1)²))+(tan(sin(cos((x²-6x+1)²))) )+(sin(tan(sin(cos((x²-6x+1)²))))) ))+sin((x²-6x+1)+(cos((x²-6x+1)²)))-(tan(sin(cos((x²-6x+1)²))))-(sin(tan(sin(cos((x²-6x+1)²)))))) )+sin((x²-6x+1)-(cos((x²-6x+1)²))+(tan(sin(cos((x²-6x+1)²))))+(sin(tan(sin(cos((x²-6x+1)²)))))) )+sin((x²-6x+1)-(cos((x²-6x+1)²))-(tan(sin(cos((x²-6x+1)²))))-(sin(tan(sin(cos((x²-6x+1)²))))) )+sin((x²-6x+1)+(cos((x²-6x+1)²))+(tan(sin(cos((x²-6x+1)²))))-(sin(tan(sin(cos((x²-6x+1)²))))) ) +sin((x²-6x+1)+(cos((x²-6x+1)²))-(tan(sin(cos((x²-6x+1)²))))+(sin(tan(sin(cos((x²-6x+1)²))))) )+sin((x²-6x+1)+(cos((x²-6x+1)²))+(tan(sin(cos((x²-6x+1)²))))-(sin(tan(sin(cos((x²-6x+1)²))))) )+sin((x²-6x+1)-(cos((x²-6x+1)²))+(tan(sin(cos((x²-6x+1)²))))-(sin(tan(sin(cos((x²-6x+1)²))))) )

try to evaluate those voodoo spell