So, I got stuck on this problem, let me know if I've done it right so far:
Use the quotient, product, and power rules of logarithms to expand the formula g(t) into three logarithmic terms. Then find g'(t) by taking the derivative of the expanded version of g.
g(t)= ln(5/t^3sec(t))
= ln(5) - ln[t^3sec(t)]
= ln(5) - 3ln(t) + ln(sec(t))
g'(t)= d/dt (5) - d/dt (3ln(t)) + d/dt(sec(t))
= 0 - [(d/dt 3 x ln(t)) + (3 x d/dt ln(t))] + [sec(t)tan(t) x d/dt (t)]
= 0 - (3/t) + (sec(t)tan(t))
= -3/7 + (sec(t)tan(t))
= (-3 + 7sec(t)tan(t)) / 7
Use the quotient, product, and power rules of logarithms to expand the formula g(t) into three logarithmic terms. Then find g'(t) by taking the derivative of the expanded version of g.
g(t)= ln(5/t^3sec(t))
= ln(5) - ln[t^3sec(t)]
= ln(5) - 3ln(t) + ln(sec(t))
g'(t)= d/dt (5) - d/dt (3ln(t)) + d/dt(sec(t))
= 0 - [(d/dt 3 x ln(t)) + (3 x d/dt ln(t))] + [sec(t)tan(t) x d/dt (t)]
= 0 - (3/t) + (sec(t)tan(t))
= -3/7 + (sec(t)tan(t))
= (-3 + 7sec(t)tan(t)) / 7