Question
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
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.
deel
yes i'm sure..the assignment like that.
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!
deel
thank's steve :)