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

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

- math -
**drwls**, Monday, August 20, 2012 at 8:35am
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.

- math -
**deel**, Monday, August 20, 2012 at 10:42am
yes i'm sure..the assignment like that.

- math -
**Steve**, Monday, August 20, 2012 at 12:00pm
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!

- math -
**deel**, Tuesday, August 21, 2012 at 4:32am
thank's steve :)

## Answer this Question

## Related Questions

- Calculus II - What is sin(i) -- (sin of the imaginary number, i) What is cos(i...
- Math/Calculus - How would I evaluate the following integral by using integration...
- Calculus - Okay so I have a question on my assignment that says: You are given ...
- Maths Calculus Derivatives - Find the first derivative for the following ...
- math - Can anyone help w/ these. 1) Solve the equation in the internal [0deg, ...
- Integral calculus - Please can anyone help with the following problems - thanks...
- Calculus - Find the outside and inside functions of the following to find their ...
- math please help - Inverse Trigonometric Functions please explain this to me in ...
- Calculus - Math questions, please help me? :(? Find the composite functions f o ...
- calculus - derivatives - can you please find the first 5 derivatives for: f(x...

More Related Questions