Derivatives

Shelled · 2014-06-02 02:37:43

Need some help with this one.

zetafunc · 2014-06-02 05:05:35

First, put

so that we can write

Now, how might we find G'(x)?

Last edited by zetafunc (2014-06-02 05:07:56)

Shelled · 2014-06-02 10:47:01

I might be misinterpreting this, so your saying

, then does that mean to get G'(x) you need to find the derivative of the stated inverse?

zetafunc · 2014-06-02 19:38:18

All I have done is noted that

by the domain-splitting property of the Riemann integral. But since I've defined F(y) as

I can write your original integral as

.

Differentiating and using the chain rule, we get (can't write apostrophes in LaTeX):

G'(x) = -sin(x)F'(cos(x)) - cos(x)F'(sin(x))

But what are F'(sin(x)) and F'(cos(x))?

Last edited by zetafunc (2014-06-02 21:19:15)

Shelled · 2014-06-04 14:32:47

Sorry about the delay; I think I've got it

?

Is the notation used okay?

Last edited by Shelled (2014-06-04 14:33:44)

zetafunc · 2014-06-04 18:04:08

You seem to have dropped the differential operator (d/dx) in lines 2 and 3, but otherwise, that looks good to me.

Last edited by zetafunc (2014-06-04 22:34:29)

Shelled · 2014-06-04 21:31:59

Alright, thank you

Math Is Fun Forum