Use the quotient rule to find the derivative of the function.

Question

3t²-1

g(t)= ¯¯¯¯¯¯¯¯¯¯

2t+5

Answer 1

Quotient rule is (g(t)•f'(t)-f(t)•g'(t))/(g(t))², where f(t) is the numerator and g(t) is the denominator.

For your problem, 3t²-1 would be f(t), and 2t+5 would be g(t).

f'(t) would be 6t, and g'(t) would be 2, using power rule. We can plug these into the formula.

((2t+5)(6t)-(3t²-1)(2))/(2t+5)²

Now, we can multiply this out and combine like terms in the numerator. I would keep the denominator as is, as it will likely not simplify well.

(12t²+30t-6t²+2)/(2t+5)²

(6t²+30t+2)/(2t+5)² would be your derivative. Hope this helps!