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Stuck on simplifying (the product rule c3)

I'm stuck on trying to simplify my answer for this question.

Find dy/dx for tanxcosx.

Here's my working so far..

ImageUploadedByStudent Room1441284645.777894.jpg




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(edited 8 years ago)
Original post by Excuse Me!
I'm stuck on trying to simplify my answer for this question.

Find dy/dx for tanxcosx.

Here's my working so far..

ImageUploadedByStudent Room1441284645.777894.jpg




Posted from TSR Mobile


With questions like this it's often helpful to get everything in terms of sin and cos.

Spoiler

Original post by Excuse Me!
I'm stuck on trying to simplify my answer for this question.

Find dy/dx for tanxcosx.

Here's my working so far..

ImageUploadedByStudent Room1441284645.777894.jpg




Posted from TSR Mobile


You're overcomplicating it! Have a careful think about what tanxcosx is equal to.
Reply 3
Original post by SeanFM
With questions like this it's often helpful to get everything in terms of sin and cos.

Spoiler



so tanx becomes sinx/cosx

what do i do with sec^2x?
Original post by Excuse Me!
so tanx becomes sinx/cosx

what do i do with sec^2x?


Apply tanx=sinx/cosx to the first line

Spoiler

Original post by Excuse Me!
so tanx becomes sinx/cosx

what do i do with sec^2x?


What is secx in terms of sin or cos?

So what is sec^2(x)?
Reply 6
Realised what tanxcosx is. Makes the question much simpler.
Reply 7
Original post by SeanFM
What is secx in terms of sin or cos?

So what is sec^2(x)?

1/cos^2x.

Think i can multiply the rest fine to simplify thanks
Original post by Excuse Me!
1/cos^2x.

Think i can multiply the rest fine to simplify thanks


Brilliant, well done :smile:
Reply 9
Original post by SeanFM
Brilliant, well done :smile:


Got to here on the question. Have I gone wrong somewhere as I'm struggling to see how I can't get cosx out of this

ImageUploadedByStudent Room1441418554.505377.jpg


Posted from TSR Mobile
Original post by Excuse Me!
Got to here on the question. Have I gone wrong somewhere as I'm struggling to see how I can't get cosx out of this




Posted from TSR Mobile


Are you sure that you've done that step correctly? Although I still think that this equation doesn't warrant a use of the product rule

Spoiler

(edited 8 years ago)
If you wanted to do it the long way, you would do it as follows:
d/dx(tanx)(cosx)
=(tanx)'(cosx) + (cosx)'(tanx)
=(sinx/cosx)'(cosx) + (-sinx)(tanx)
=((cos^2x-(sin^2x))/cos^2x)(cosx) - (sinx)(tanx)
=((cos^2x/cos^2x)+(sin^2x/cos^2x))(cosx) - (sinx)(tanx)
=((cos^3x/cos^2x)+((sin^2x)(cosx)/cos^2x))) - (sinx)(sinx/cosx)
=(cosx+(sin^2x/cosx)) - (sin^2x/cosx)
=cosx

As you can see, that's rather long winded and you can see why everyone prefers to just simplify (tanx)(cosx) to sinx in the first step.
Original post by Excuse Me!
Got to here on the question. Have I gone wrong somewhere as I'm struggling to see how I can't get cosx out of this

ImageUploadedByStudent Room1441418554.505377.jpg


Posted from TSR Mobile


tanx * sinx isn't cosx, it's (sinx)^2/cosx
ImageUploadedByStudent Room1441483955.083069.jpg

Now up to here. Quite confused.

I understand the simpler method but have to do it by the product rule


Posted from TSR Mobile
Go back a few steps and consider that sec^2x= 1+tan^2x
Then multiply that by the cosx to get cosx+ tan^2xcosx
Then make that tan^2xcosx = sin^2xcosx/cos^2x
Divide that through by cosx and you'll notice that the negative version of that is what you have over to the left. Therefore, they cancel out and you're left with cosx.
(edited 8 years ago)

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