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Posted by on Monday, August 20, 2012 at 8:29am.

find the derivatives, dy/dx, for the following functions :

y=(1+sin^2{2 exp (3x)})^5y

please help me to solve this assignment.

thank's

  • math - , Monday, August 20, 2012 at 8:35am

    Are you sure the right hand of the equation ends with y? If so, you do not have an explicit y(x) function.

    It can be differentiated implicitly, but is rather a mess.

  • math - , Monday, August 20, 2012 at 10:42am

    yes i'm sure..the assignment like that.

  • math - , Monday, August 20, 2012 at 12:00pm

    wow. that's a nasty one.

    Recall that, extending the power and exponent rules, if u and v are functions of x, then if

    y = u^v
    dy/dx = v*u^(v-1) du/dx + ln(u) * u^v * dv/dx

    So, letting
    u = 1+sin^2(2e^3x)

    y = u^5y
    y' = 5y * u^(5y-1) u' + ln(u) * u^5y * 5y'

    Now, u' = 2sin(2e^3x)cos(2e^3x)*(6e^3x)

    and I'm sure you can take it from there. Good luck!

  • math - , Tuesday, August 21, 2012 at 4:32am

    thank's steve :)

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