Posted by Daisy on Thursday, October 3, 2013 at 3:52am.
Find the derivatives of:
1. H(x)= sin2xcos2x
The answer given is 2cos4x. My question is, how in the world did they get that!? Shouldn't the answer at least contain the sin function, either negative or positive seeing as it's the derivative of cos? Also, which rules are involved in this problem? Product and chain rule?
2. f(x)= (cotx) / (sinx)
I ended up with a mess of an answer that no where near resembled the solution.
Any help would be greatly appreciated! :)

Derivatives  Steve, Thursday, October 3, 2013 at 4:58am
H(x) = sin2x cos2x
= 1/2 sin4x
That help?
Using the product rule, it's a bit more work, but you can get the same answer:
dH/dx = 2cos2x cos2x  2sin2x sin2x
= 2(cos^2 2x  sin^2 2x)
= 2cos4x
Don't forget your trig just because you're taking calculus!
#2
df/dx = (u'v  uv')/v^2
= (csc^2 * sin  cot * cos)/sin^2
= (csc  cos^2/sin)/sin^2
= 1/sin^3  cot^2 csc
= csc(csc^2+cot^2)
or, getting rid of the pesky cot,
f = cos/sin^2
f' = (sin^3  2cos^2*sin)/sin^4
= (sin^2  2cos^2)/sin^3
= (1+cos^2)/sin^3
= csc(csc^2+cot^2)
Answer This Question
Related Questions
 Calculus  Okay so I have a question on my assignment that says: You are given ...
 Calculus  show that the curves r=asin(è) and r=acos(è) intersect at right ...
 Calculus  Find the derivatives of the function k(x)=sqrt(sin(2x))^3 I think I ...
 math  I studied derivatives before, but kind of forgot them all, is there a ...
 calculus  1.) values of f(t) are given in the following table: t 0 2 4 6 8 10 f...
 calculus  Let f be a function that has derivatives of all orders for all real ...
 convert derivatives of x,y,z, to r, Ɵ,z  convert derivatives of x,y,z, to ...
 extrema  The function is given as y = 7x^3  8x^2 16x +15 The max is at x = 4...
 math  find the derivatives, dy/dx for the folowing function : y=ln(cos(0.5)+(...
 Calculus  Find a formula for the derivatives of the function m(x)=1/(x+1) IS ...
More Related Questions