find the derivative of f(x) = arcsin(-x)

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- Nov 8th 2006, 01:48 PMmyoplex11inverse trigonometric differentiation
find the derivative of f(x) = arcsin(-x)

- Nov 8th 2006, 01:56 PMAfterShock
- Nov 8th 2006, 02:11 PMJameson
Draw a triangle such that . Add the hypotenuse and then differentiate both sides of this equation, remembering y is a function of x.

- Nov 8th 2006, 02:16 PMSoroban
Hello, myoplex11!

No logs are involved in this problem . . .

Quote:

Find the derivative of:

As AfterShock pointed out, there is a standard formula for arcsine.

If you are expected to*derive*this formula, you can do it . . .

We have: .

Take the sine of both sides: .

Differentiate implicitly: .

Since , .Pythagorus tell us that:

. . Hence:

And the formula becomes: .

- Nov 8th 2006, 05:06 PMThePerfectHacker
The composite function,

Now there is a theorem that says that is differenciable function so use the chain rule,

Thus,

So to find,

derivative use what AfterShock said.