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