calculus

posted by .

find the derivative of f(x)=cot(3x)csc^2(3x)

  • calculus -

    f(x)=cot(3x)csc^2(3x) = cosx/sin^3x

    Let sinx = u . Then du = cosx dx

    The integral of f(x) becomes

    Integral of du/u^3 = -(1/2) u^-2
    = (-1/2)(1/sinx)^2
    = (-1/2)csc^2x

  • calculus -

    first change it to
    f(x) = cos 3x/(sin 3x)^3 like drwls had

    now use the quotient rule to find f'(x)

    f'(x) = [(sin 3x)^3(-3)(sin 3x) - 3(sin 3x)^2(cos 3x)(3)(cos 3x)]/(sin 3x)^6
    = -3[(sin 3x)^2 + 3(cos 3x)^2]/(sin 3x)^4

  • calculus -

    I made at least one mistake. The first was using x instead of 3x.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Chain Rule

    Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x ã3x …
  2. Calculus

    Hello, I'm having trouble with this exercise. Can you help me?
  3. Calculus

    yes! tnk u ok? It's actually (x->0.) Find the limit of cot(x)-csc(x) as x approached 0?
  4. Calculus

    Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x ã3x …
  5. Calculus

    Any help would be much appreciated with the steps involved in each problem given. Thank you. 1) Find derivative if y =cot x + sin x 2) Find derivative if y = (3x+5)^8 3) Find derivative if y = x csc x 4) Find derivative if y = x /3x …
  6. Trigonometry

    Hello all, In our math class, we are practicing the trigonometric identities (i.e., sin^2(x)+cos^2(x)=1 or cot(x)=cos(x)/sin(x). Now, we are working on proofs that two sides of an equation are equal (for example, sin(x)*csc(x)=1; sin(x)csc(x)=sin(x)/sin(x)=1; …
  7. Math - Trig

    I'm trying to verify these trigonometric identities. 1. 1 / [sec(x) * tan(x)] = csc(x) - sin(x) 2. csc(x) - sin(x) = cos(x) * cot(x) 3. 1/tan(x) + 1/cot(x) = tan(x) + cot(x) 4. csc(-x)/sec(-x) = -cot(x)
  8. Trig verifying identities

    I am having trouble with this problem. sec^2(pi/2-x)-1= cot ^2x I got : By cofunction identity sec(90 degrees - x) = csc x secx csc-1 = cot^2x Then split sec x and csc-1 into two fractions and multiplied both numerator and denominators …
  9. trig

    verify (csc^4-1)/cot^2x=2+cot^2x So this is what I have so far on the left side (csc^2x+1)(cscx+1)(cscx-1)/cot^2x =(csc^2x+1)(cot^2x)/cot^2x i think I'm doing something wrong. Please help!
  10. Math

    Find an equation for the tangent line to the curve at (π/2 , 2). y = 4 + cot(x) - 2csc(x) I am confused how to take the derivative of this problem. When I tried to solve it I ended up with -csc^2 (x) + (2csc(x) * cot(x)). From …

More Similar Questions