Post a New Question

calculus

posted by .

Differentiate.

y= (cos x)^x

u= cos x
du= -sin x dx

ln y = ln(cos x)^x
ln y = x ln(cos x)

(dy/dx)/(y)= ln(cos x)
(dy/dx)= y ln(cos x)
= (cos x)^x * (ln cos x)

(dx/du)= x(cos x)^(x-1) * (-sin x)
= - x sin(x)cos^(x-1)(x)

(dy/dx)-(dx/du)= [(cos^x(x))(ln(cos(x)))-(x sin(x)cos^(x-1)(x)]

(dy/du)= cos^x(x)*(ln(cos(x)))-(x tan(x))

Is this correct?

Also, I am stuck on a different problem.

Differentiate.

y= arctan(arcsin(sqrt(x)))

u= arcsin(sqrt(x))
du= (1/(sqrt(1-x^2))) dx

ln y = ln ?? do I put the whole original here?

  • calculus -

    ln y = x ln(cos x) I agree.

    y'/y=x/cosx + ln(cosx) which changes the rest.

    check that.

    I would do the next this way.

    y= arctan u
    y'=d(arctan u) du
    now u= arcsin(z)
    du= d arcsinZ dz
    and z= sqrtX
    dz= 1/2sqrtX dx

    so do that substitution, and you are done.

  • calculus -

    I'm sorry, but I'm confused on the 2nd part?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. trig

    Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The quantity …
  2. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b) …
  3. algebra

    Can someone please help me do this problem?
  4. pre-cal

    Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x -48
  5. Mathematics - Trigonometric Identities

    Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) = (sin^2y …
  6. Math - Solving Trig Equations

    What am I doing wrong? Equation: sin2x = 2cos2x Answers: 90 and 270 .... My Work: 2sin(x)cos(x) = 2cos(2x) sin(x) cos(x) = cos(2x) sin(x) cos(x) = 2cos^2(x) - 1 cos(x) (+/-)\sqrt{1 - cos^2(x)} = 2cos^2(x) - 1 cos^2(x)(1 - cos^2(x))
  7. TRIG!

    Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x + cos^6 …
  8. Precal

    I do not understand how to do this problem ((sin^3 A + cos^3 A)/(sin A + cos A) ) = 1 - sin A cos A note that all the trig terms are closed right after there A's example sin A cos A = sin (A) cos (A) I wrote it out like this 0 = - …
  9. Calc.

    Differentiate. y= (cos x)^x u= cos x du= -sin x dx ln y = ln(cos x)^x ln y = x ln(cos x) (dy/dx)/(y)= ln(cos x) (dy/dx)= y ln(cos x) = (cos x)^x * (ln cos x) (dx/du)= x(cos x)^(x-1) * (-sin x) = - x sin(x)cos^(x-1)(x) (dy/dx)-(dx/du)= …
  10. math

    Determine exact value of cos(cos^-1(19 pi)). is this the cos (a+b)= cos a cos b- sina sin b?

More Similar Questions

Post a New Question