How can I find the derivative of this implicit relation?
How do I find dG/dt for G=(bv)/(1-(v^2/c^2))^(1/2)
*b and c are constants
*v depends on t
I would really appreciate if you explained it to me so I can learn how to solve such problems.
Thanks!
How can I find the derivative of this implicit relation?
How do I find dG/dt for G=(bv)/(1-(v^2/c^2))^(1/2)
*b and c are constants
*v depends on t
I would really appreciate if you explained it to me so I can learn how to solve such problems.
Thanks!
Since v is a function of t, this is a composition of functions, with your "inner" function of t being v(t), and your "outer" function of v being $\displaystyle \displaystyle \begin{align*} \frac{b\,v}{\sqrt{1 - \frac{v^2}{c^2}}} \end{align*}$. So to differentiate this function with respect to t, you need to use the chain rule and differentiate both the inner and outer functions, then multiply them together.
The derivative of the inner function is $\displaystyle \displaystyle \begin{align*} \frac{dv}{dt} \end{align*}$. I'll leave you to evaluate the derivative of the outer function.