Derivative of F(t): Solving Doppler Shift Problem

[chlorine]

Homework Statement

This problem has to do with Doppler shifts as frequency changes with time.
F(t)=fo(1-(v^2*T)/(c*sqrt(v^2*T^2+b^2))
T=t-To
I want to find F'(t) .

Homework Equations

See #1.

The Attempt at a Solution

I expand F(t) to be
F(t)=f0-(fo*v/c)*(1+(b/(vT))^2)^1/2
and again...
F(t)=f0-(fo*v/c)*(1+b^2*v^-2*T^-2)^1/2

After this, I forgot all of my calculus I've learned couple years ago. :(
Please help me remember what to do.
I know you do exponent on the outside and then work inside... dot dot dot.

Thanks.

 

[Mark44]

Homework Statement

This problem has to do with Doppler shifts as frequency changes with time.
F(t)=fo(1-(v^2*T)/(c*sqrt(v^2*T^2+b^2))
T=t-To
I want to find F'(t) .

Homework Equations

See #1.

The Attempt at a Solution

I expand F(t) to be
F(t)=f0-(fo*v/c)*(1+(b/(vT))^2)^1/2

The above is incorrect for a number of reasons. I don't know what you did to get this. Don't bother multiplying by f₀.

and again...
F(t)=f0-(fo*v/c)*(1+b^2*v^-2*T^-2)^1/2

After this, I forgot all of my calculus I've learned couple years ago. :(
Please help me remember what to do.
I know you do exponent on the outside and then work inside... dot dot dot.

Thanks.

You need to use the quotient rule first, and you will need the chain rule to get the derivatives that arise in the quotient rule.