Question

Find the indicated derivative. yequalsStartFraction t squared plus 3 Over left parenthesis 7 t minus 5 right parenthesis Superscript 5 EndFraction StartFraction d Over dt EndFraction left parenthesis StartFraction t squared plus 3 Over left parenthesis 7 t minus 5 right parenthesis Superscript 5 EndFraction right parenthesis ​= nothing

Answer 1

Answer:

$y'=\frac{7t^2-10t-21}{(7t-5)^2}$

Step-by-step explanation:

We have been given a function $y=\frac{t^2+3}{7t-5}$. We are asked to find the derivative of the given function.

We will use quotient rule of derivatives to find derivative of our given function.

$\frac{d}{dx}(\frac{f(x)}{g(x)})=\frac{f'(x)g(x)-f(x)g'(x)}{(g(x))^2}$

$y'=\frac{\frac{d}{dt}(t^2+3)\cdot (7t-5)-\frac{d}{dt}(7t-5)\cdot(t^2+3)}{(7t-5)^2}$

$y'=\frac{(2t)\cdot (7t-5)-7\cdot(t^2+3)}{(7t-5)^2}$

$y'=\frac{14t^2-10t-7t^2-21}{(7t-5)^2}$

$y'=\frac{7t^2-10t-21}{(7t-5)^2}$

Therefore, our required derivative would be $y'=\frac{7t^2-10t-21}{(7t-5)^2}$.