F(t) = square root of 3t+2 / 4t-3

[kim]

Need to find the derivative of:

f(t) = square root of 3t+2 / 4t-3

please help.

 

[Hurkyl]

What have you tried?

 

[mathmike]

is this sqrt{3t+2 / 4t-3} or sqrt{3t+2} / 4t-3

 

[bomba923]

Well, decide whether

is this sqrt{3t+2 / 4t-3} or sqrt{3t+2} / 4t-3

And the Quotient Rule will help you solve this problem~!!
$$\frac{d}{{dt}}\left[ {\frac{{f\left( t \right)}}{{g\left( t \right)}}} \right] = \frac{{f'\left( t \right)g\left( t \right) - f\left( t \right)g'\left( t \right)}}{{\left[ {g\left( t \right)} \right]^2 }}$$

 

[Jameson]

Or the product rule... :)

$$\sqrt{3t+2}*(4t-3)^{-1}$$

 

[R_Y_A_N]

or do implicit differentiation:
let y = sqrt(3t + 2)/(4t-3)
and then (4t-3)y = sqrt(3t+2)

 

[Jameson]

Well, touche then. I'll think of something more clever later...

 

[R_Y_A_N]

while you are thinking of something else...here's another idea:
logarithmic differentiation
lny = (1/2)ln(3t+2) - ln(4t-1)