Asked by deel

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

Answers

Answered by drwls
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.
Answered by deel
yes i'm sure..the assignment like that.
Answered by Steve
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!
Answered by deel
thank's steve :)
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