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
            
        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.
    
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!
    
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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