Posted by deel 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  drwls, 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  deel, Monday, August 20, 2012 at 10:42am
yes i'm sure..the assignment like that.

math  Steve, 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^(v1) du/dx + ln(u) * u^v * dv/dx
So, letting
u = 1+sin^2(2e^3x)
y = u^5y
y' = 5y * u^(5y1) 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  deel, Tuesday, August 21, 2012 at 4:32am
thank's steve :)