# Derivatives

posted by .

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 -

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)

## Similar Questions

1. ### Calculus

Okay so I have a question on my assignment that says: You are given that tan(y) = x. Find sin(y)^2. Express your answer in terms of x. I know its derivatives, and I've tried taking the derivatives of both etc, and got them both to …
2. ### extrema

The function is given as y = 7x^3 - 8x^2 -16x +15 The max is at x = -4/7 & min is at x = 4/3 How do I know that it is local max&min or absolute max &min?
3. ### calculus

Let f be a function that has derivatives of all orders for all real numbers. Assume f(0)=5, f'(0)=-3, f''(0)=1, and f'''(0)=4. Write the third-degree Taylor polynomial for h, where h(x) = integral of f(t)dt from 0 to x, about x=0 for …
4. ### Calculus

show that the curves r=asin(è) and r=acos(è) intersect at right angles. can you show that the derivatives for each are the negative reciprocal of each other?
5. ### Calculus

Find a formula for the derivatives of the function m(x)=1/(x+1) IS the answer -1/(x+h)(x+h+1)
6. ### math

I studied derivatives before, but kind of forgot them all, is there a website that gives me an overview of derivatives. What is first and second derivatives, how to find it, all the derivative rules and so on... thank you
7. ### convert derivatives of x,y,z, to r, Ɵ,z

convert derivatives of x,y,z, to r, Ɵ,z with chain rule?
8. ### calculus

1.) values of f(t) are given in the following table: t 0 2 4 6 8 10 f(t) 137 112 88 68 49 34 a. Does this function appear to have a positive or negative first derivative?
9. ### math

find the derivatives, dy/dx for the folowing function : y=ln(cos(0.5)+(sin(x^2+3))^1/3)
10. ### Calculus

Find the derivatives of the function k(x)=sqrt(sin(2x))^3 I think I have the answer and was wondering if i had it correct k'(x)=2sin(x)^3+8sin(x)

More Similar Questions