Differentiation 3

[IloveManUtd]

In my question:

Differentiate 1/sqrt(a[sup:2uwf4kg9]2[/sup:2uwf4kg9] - 2x) with respect to x. I've changed (a[sup:2uwf4kg9]2[/sup:2uwf4kg9] -2x) to (a[sup:2uwf4kg9]2[/sup:2uwf4kg9] -2x)[sup:2uwf4kg9]-1/2[/sup:2uwf4kg9]. What next?

 

[mmm4444bot]

What next? Use the Chain Rule.

Here's an example: (3x^2 - 7x)^(1/2)

This is a composite function; the outer function is (____)^(1/2), and the inner function is 3x^2 - 7x.

The Chain Rule tells us that the derivative of this example is the product of the outer function's derivative times the inner function's derivative.

So, we need to determine these two derivatives and then multiply them together.

To differentiate the outer function, ignore the inner function momentarily (because it's not involved) and apply the Power Rule.

(1/2)*(____)^(1/2 - 1)

(1/2)*(____)^(-1/2)

The derivative of the outer function is (1/2)(3x^2 - 7x)^(-1/2)

To differentiate the inner function, also use the Power Rule.

2*3*x^(2 - 1) - 1*7*x^(1 - 1)

2*3x^1 - 7*x^0

The derivative of the inner function is 6x - 7

Now, multiply the two derivatives together.

(1/2)(3x^2 - 7x)^(-1/2) * (6x - 7)

We can also write this answer as: (6x - 7)/[2 sqrt(3x^2 - 7x)]

Do you have any specific questions ?

 

[BigGlenntheHeavy]

\(\displaystyle I'm \ suppose \ to \ add \ 2 \ and \ 5. \ What's \ next?\)

 

[Denis]

\(\displaystyle I'm \ suppose \ to \ add \ 2 \ and \ 5. \ What's \ next?\)

Result will be less than 10, so use your fingers :idea:

 

[mmm4444bot]

use your fingers

No, Denis. I think the answer is "find someone to do it for you" because that's so much easier than using your fingers.