how to deal with fractional exponents when using the quotient rule to find the derivative. (correct my logic please)

Question

The question states y(t)=(√t)/(t^2  +1) find y'(t)

So I got (-(3/2)t)/2(t^2  +1)^2 but that was wrong so I think I oversimplified my derivative. I went back a step and put

(-(3/2)t^(3/2)+(1/2))/t^(1/2)(t^2 +1)^2

but that was wrong as well. Please help me figure out where I went wrong.

Answer 1

Phil, when you have a fractional exponent, finding the derivative is still the same because a fraction is like any other constant.

 

In our problem, we have √t = t^1/2

 

The derivative of t^1/2 = 1/2 (t^{1/2 - 1}) = 1/2 (t^-1/2)

 

or 1/(2√t)

 

Now do you see where you made your error?

 

The Quotient Rule states that given f(x)/g(x), its derivative is:

 

[g(x)f'(x) - f(x)g'(x)] ÷ (g(x))²