Dal J. answered • 02/26/15

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The answer to the first two is about like - "I run out of fingers to count on". Basically, the problem is too hairy and contains components that don't play nice using those rules. You need to explain what those components are.

Okay, I'm going to skip straight to the third one. Let's rephrase "the square root of X" to be X raised to the 1/2 power.

Y = (sqrt(x))

^{X }= ( X^{(1/2) })^{X }= X^{(1/2)*X}= X^{X/2}Now, that's almost something we can work with.

Now, remember that X = e

^{ logX}, SoY = X

^{X/2}= (e^{ logX})^{X/2}= e^{X/2*logX}In that form, you can use the exponential derivative rule and then the product rule to get Y'.

When Y = e

^{f(x)}Then Y' = f'(x)*e^{f(x)}(the exponential derivative rule)All you have to do is find the derivative of X/2*log(X)

Remember that when H(X) = F(X)G(X) then H'(X) = F(X)G'(X) + F'(X)G(X) (the product rule)

Can you solve it now?

Dal J.

02/26/15