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^(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 -
**deel**, Tuesday, August 21, 2012 at 4:32am
thank's steve :)

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