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C3 Differentiation watch

1. Given that x= 4sin(2y+6), find dy/dx in terms of x.
2. Easy first you need to differentiate dx/dy NOT dy/dx

x=4sin(2y+6)

dx/dy=4x2cos(2y+6) remember sinf(x)=f'(x)cosf(x)

dx/dy=8cos(2y+6) >> dy/dx=1/8cos(2y+6)
3. (Original post by Remarqable M)
Easy first you need to differentiate dx/dy NOT dy/dx
But it wants the answer in terms of x, the equation is given in terms of y.
But it wants the answer in terms of x, the equation is given in terms of y.
Re-arrange the equation to make it in terms of x, and substitute it back into the differential.
5. (Original post by Mathematician!)
Re-arrange the equation to make it in terms of x, and substitute it back into the differential.
is my answer correct? did i do something wrong?
6. (Original post by Remarqable M)
is my answer correct? did i do something wrong?
Your answer is correct, but it's incomplete (as the OP has pointed out).
7. (Original post by Mathematician!)
Your answer is correct, but it's incomplete (as the OP has pointed out).
could you do this question both for me and OP please in latex form
8. ORIGINAL QUESTION: x= 4sin(2y+6), find dy/dx in terms of x.

Spoiler:
Show

And as ,

9. (Original post by Mathematician!)
ORIGINAL QUESTION: x= 4sin(2y+6), find dy/dx in terms of x.

Spoiler:
Show

And as ,

The answer should not include cos or the inverse of sin. What would the answer be without them.
The answer should not include cos or the inverse of sin. What would the answer be without them.

Now

So,

Use the chain rule here, by substituting .

So

These utilise simple differentiation, and the general rule for the differential of inverse sine functions (though it can be derived using trigonometric identities. Ask me if you want me to show this).

I'll leave the rest to you.
11. (Original post by Mathematician!)

Now

So,

Use the chain rule here, by substituting .

So

These utilise simple differentiation, and the general rule for the differential of inverse sine functions (though it can be derived using trigonometric identities. Ask me if you want me to show this).

I'll leave the rest to you.
Although not covered in C3(the differential of inverse sine functions), I appreciate your working and the effort you've put into explaining this simple differentiation, which i will need in the future ofcourse I will try this alternative method out it looks simple. Thanks again
12. (Original post by Remarqable M)
Although not covered in C3(the differential of inverse sine functions), I appreciate your working and the effort you've put into explaining this simple differentiation, which i will need in the future ofcourse I will try this alternative method out it looks simple. Thanks again
Well I can show you how it works! It is rather simple (when you know how! ) Open the following spoiler if you would like to see how it's done...

Spoiler:
Show
Let

It follows, of course, that

So using either implicit differentiation, or direct differentiation, you get

Now this can be reduced further, as we know that

So this re-arranges to give

Now using , it follows that

This can be subsituted into the differential to give
13. (Original post by Mathematician!)
Well I can show you how it works! It is rather simple (when you know how! ) Open the following spoiler if you would like to see how it's done...

Spoiler:
Show
Let

It follows, of course, that

So using either implicit differentiation, or direct differentiation, you get

Now this can be reduced further, as we know that

So this re-arranges to give

Now using , it follows that

This can be subsituted into the differential to give
thanks it makes sense now, how the rule is derived.

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