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January 27, 2015

January 27, 2015

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

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

please help me to solve this assignment.

thank's

- math -
**drwls**, Monday, August 20, 2012 at 8:35amAre 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 10:42amyes i'm sure..the assignment like that.

- math -
**Steve**, Monday, August 20, 2012 at 12:00pmwow. 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 4:32amthank's steve :)

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