Calculus

How to derive cosh (3x) in terms of cosh (x) and sinh (x) ? Initially I start with 1/2 (e^3x+e^-3x) but I'm stuck from there because I don't know how to continue... :(

  1. 👍
  2. 👎
  3. 👁
  1. Using the chain rule:

    u = 3 x

    du = 3 dx Divide both sides by 3

    du / 3 = dx

    dx = du / 3

    d cosh ( 3 x ) / dx =

    d cosh ( u ) / ( du / 3 ) =

    3 d cosh ( u ) / du

    d cosh ( u ) / du = sinh u

    so

    d cosh ( 3 x ) / dx = 3 d cosh ( u ) / du = 3 sinh u = 3 sinh ( 3 x )

    1. 👍
    2. 👎
  2. cosh(3x) = cosh(2x+x)
    = cosh2x coshx + sinh2x sinhx
    ...

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. Physics

    A proton, moving with a velocity of vi, collides elastically with another proton that is initially at rest. Assuming that after the collision the speed of the initially moving proton is 2.90 times the speed of the proton initially

  2. Calculus

    A steady wind blows a kite due west. The kite's height above ground from horizontal position x = 0 to x = 60 ft is given by y = 150 − 1/40(x − 50)^2. Find the distance traveled by the kite. (Round your answer to one decimal

  3. Physics

    Hi guys, Im a bit stumped on how to solve an online physics homework problem and it's really bothering me. I have no idea how to come up with the angles or even attempt the problem and neither do my friends. We'd all really

  4. Calculus 1

    Find the numerical value of each expression. (Round your answers to five decimal places.) (a) cosh 9 (b) cosh(ln 9)

  1. Math

    Find the derivatives of the function g(t)= cosh^3 t.

  2. Calculus 1

    If tanh x=4/5, find the values of the other hyperbolic functions at x. sinh x= cosh x= coth x= sech x= csch x=

  3. Calculus 12th grade (double check my work please)

    1.)Find dy/dx when y= Ln (sinh 2x) my answer >> 2coth 2x. 2.)Find dy/dx when sinh 3y=cos 2x A.-2 sin 2x B.-2 sin 2x / sinh 3y C.-2/3tan (2x/3y) D.-2sin2x / 3 cosh 3yz...>> my answer. 2).Find the derivative of y=cos(x^2) with

  4. physics

    Derive a formula for the maximum speed vmax of a simple pendulum bob in terms of g, the length ℓ, and the maximum angle of swing θmax. Express your answer in terms of the variables g, l, and θmax.

  1. Calc 1

    Find the derivative dy/dx y=e^(sinh(x))

  2. Calculus Please Help

    Let y(x)=ln(cosh(x)+ sqrt(cosh^2(x)−1)) Find the derivative Dxy= I don't know what to do with this...

  3. AP Physics

    I'm trying to derive the formula v^2 = v0^2 + 2a(x-x0) were zeros are subscripts my book tells me to derive it this way use the definition of average velocity to derive a formula for x use the formula for average velocity when

  4. Calculus

    Let y(x)=ln(cosh(x)+ sqrt(cosh^2(x)−1)) Find the derivative Dxy= I don't know what to do with this...

You can view more similar questions or ask a new question.