Calculating the derivative

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mathhelp418

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Oct 23, 2012
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I have the problem

f(x) = sqrt(1/x^17)

I am supposed to calculate the derivative but do not know how with the sqrt.

Thanks in advance!
 
I would try to get rid of the square root. Put the whole equation to the power of 1/2 and then apply the power rule.

:)
 
Young said:
I would try to get rid of the square root. Put the whole equation to the power of 1/2 and then apply the power rule.

:)
Click to expand...
Use the exponent 1/2 instead of the Square Root sign. Do that to the RHS (right hand side) of the equation.
When you modify that expression, you will add additional values (but we'll discuss that later)

For now,
f(x) = sqrt(1/x^17)
becomes
f(x) = (1/x^17) ^(1/2)
before you take the derivative, can you combine these exponents?
 
mathhelp418 said:
So I got

1 ^ (3/2)
____________

x ^ 16/2

But I don't think I am doing it right...
Click to expand...

I can't imagine why you would write "1^(3/2)" rather than just 1! In any case, the point is that your function is \(\displaystyle x^{-17/2}\). Now use the fact that the derivative of \(\displaystyle x^n\) is \(\displaystyle nx^{n-1}\).
 
\(\displaystyle y = \sqrt{\frac{1}{x^{17}}}\)

\(\displaystyle y = \sqrt{x^{-17}}\)

\(\displaystyle y = x^{-17/2}\)

Taking the derivative

\(\displaystyle y = \frac{-17}{2}(x)^{-19/2}\)

or

\(\displaystyle y = \frac{-17}{2}\sqrt{x^{-19}}\)

Is this right?
 
Last edited:
Yes, all of \(\displaystyle \frac{-17}{2}\sqrt{x^{-19}}\), \(\displaystyle -\frac{17}{2}x^{-19/2}\), and \(\displaystyle -\frac{17}{2\sqrt{x^19}}\) are equal and valid answers to this problem.

Since the function was originally given as \(\displaystyle \sqrt{\frac{1}{x^{17}}}\), I think I would give the answer as \(\displaystyle -\frac{17}{2}\sqrt{\frac{1}{x^{19}}}\), in that same form.
 
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