How do you get the derivative of radical functions?

Question

Given the equation 1/ square root of (x+2), how??? Please show how using the rules of differentiation and not using them. Radical Functions are pretty much the only type of function I don't know how to get the derivative of. I'm taking the test on derivatives soon, so PLEASE HELP!!!!!!!!!!! Thank You!

Answer 1

Remember that radical functions can be expressed as to the power of 1/2. Then, all we have to do is use the power rule.

Let's take your example.

f(x) = 1/sqrt(x+2)

This is equal to

f(x) = 1/(x+2)^(1/2)

Which then becomes

f(x) = (x+2)^(-1/2)

Now, use the power rule.

f'(x) = (-1/2)(x+2)^[-3/2] (1)

Answer 2

First, get rid of the radicals and express things in terms of fractional powers. Something like cube root of x² becomes x^(2/3) which is *much* easier to handle using the power rule.


Doug

Answer 3

you do no longer desire that formula. Rewrite it y= (x-7) ^ (a million/2) Then stick on your regulations of taking derivatives, deliver the (a million/2) to the front, subtract one from the ability. you're able to get a million over (2 sqrt (x-7)). solid success.