Post a New Question

math

posted by .

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 -

    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 -

    yes i'm sure..the assignment like that.

  • math -

    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 -

    thank's steve :)

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Calculus

    Okay so I have a question on my assignment that says: You are given that tan(y) = x. Find sin(y)^2. Express your answer in terms of x. I know its derivatives, and I've tried taking the derivatives of both etc, and got them both to …
  2. math

    Can anyone help w/ these. 1) Solve the equation in the internal [0deg, 360deg]. a) sin 2x = -sin x b) sin 2T = -1/2 (where T is angle) c) 4 sin^2T = 3 2) Evaluate the expression. sin(arctan 2) 3) Rewrite the following w/o using trigonometric …
  3. Calculus II

    What is sin(i) -- (sin of the imaginary number, i) What is cos(i)-- cosine of the imaginary number, i orrr tan(1+i) You can derive these things from the equation: Exp(i x) = cos(x) + i sin(x) ---> sin(x) = [Exp(ix) - Exp(-ix)]/(2i) …
  4. Integral calculus

    Please can anyone help with the following problems - thanks. 1) Integrate X^4 e^x dx 2) Integrate Cos^5(x) dx 3) Integrate Cos^n(x) dx 4) Integrate e^(ax)Sinbx dx 5) Integrate 5xCos3x dx The standard way to solve most of these integrals …
  5. Math/Calculus

    How would I evaluate the following integral by using integration by parts?
  6. calculus - derivatives

    can you please find the first 5 derivatives for: f(x) = (0.5e^x)-(0.5e^-x) f'(x) = ?
  7. math please help

    Inverse Trigonometric Functions please explain this to me in mathematical steps please how to solve sin^(-1) (-1/2) this equals - pi/6 i know that sin^(-1) domain and range switch from original sin but i don't know how to apply that... …
  8. Maths Calculus Derivatives

    Find the first derivative for the following functions 1) f(x) = sin(cos^2x) cos(sin^3x) 2) f(x) = ( tan 2x - tan x ) / ( 1 + tan x tan 2x ) 3) f(x) = sin { tan ( sqrt x^3 + 6 ) } 4) f(x) = {sec^2(100x) - tan^2(100x)} / x
  9. Calculus

    Find the outside and inside functions of the following to find their derivatives: 1) sqrt(2x+9) 2) cos(cos(x)) 3) tan(x) I already know how to find their derivatives I'm just not exactly sure what parts of the chain rule equation would …
  10. math

    Find the derivatives of the following functions. 1.F (x)cotx 2.f (x)=sin (x2+2)

More Similar Questions

Post a New Question