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

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

please help me to solve this assignment.


  • math -

    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 -

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

  • math -

    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 -

    thank's steve :)

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