Posted by jackie on Tuesday, December 8, 2009 at 6:26pm.
find the derivative of f(x)=cot(3x)csc^2(3x)

calculus  drwls, Tuesday, December 8, 2009 at 6:33pm
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  Reiny, Tuesday, December 8, 2009 at 7:45pm
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  drwls, Tuesday, December 8, 2009 at 9:47pm
I made at least one mistake. The first was using x instead of 3x.
Answer This Question
Related Questions
 Calculus  Any help would be much appreciated with the steps involved in each ...
 Calculus  Any help would be much appreciated with the steps involved in each ...
 trig  verify (csc^41)/cot^2x=2+cot^2x So this is what I have so far on the ...
 Trig verifying identities  I am having trouble with this problem. sec^2(pi/2x...
 Chain Rule  Any help would be much appreciated with the steps involved in each ...
 Trigonometry  Hello all, In our math class, we are practicing the trigonometric...
 Calculus  Hello, I'm having trouble with this exercise. Can you help me? ...
 Math  Find an equation for the tangent line to the curve at (π/2 , 2). y...
 Calculus  yes! tnk u ok? It's actually (x>0.) Find the limit of cot(x)csc(...
 Math  Trig  I'm trying to verify these trigonometric identities. 1. 1 / [sec(x...
More Related Questions