Math Is Fun Forum

aizeltine

Member

Registered: 2011-12-21

Posts: 2

I need help in calculus?

Can you please explain and show the steps of the ff.?
1. Find the derivative of the ff. f(x) = cos^5(2x^6)
2. Suppose f(1) = 2, f '(1) = 3 and f '(2) =4, then f^-1(2)=?
3. Find an equation of the tangent line to the curve 2x^3 + 2y^3 -9xy= 0 at the x coordinate 1.
4. Find all points on the curve 2x^3 + 2y^3 -9xy= 0 where you will have a horizontal and vertical tangent lines.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: I need help in calculus?

Hi;

For question1)

Have you learned the chain rule? if not here is an example.

Your equation  is

The chain rule says:

1) Start with the substitution of u = 2x^6 then

So we have one term of the chain rule, we need the other.

Don't know how to differentiate that? No problem! Use the chain rule again at no extra charge!.

2) Make a substitution of z = cos(u).

Using the substitution in 2) we y = z^5.

Now we have both terms we need for B) so just plug in to B.

Now we have the dy/du we needed for A so just plug in there.

Now we have picked up a whole mess of substitutions while we were differentiating so let's clean them up. We know from 1) the u = 2x^6.

We know from 2) the z=cos(u) which equals z = cos(2x^6).

We are done!

For question3)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.