Question

How do you differentiate `f(t)= sqrt(t) / (-4t-6)` using the quotient rule?

Answer 1

`f'(t)=frac{2t-3}{(sqrtt)(-4t-6)^2}`

Explanation:

`f(t)=frac{sqrtt}{-4t-6}`

`f(t)=frac{t^(1/2)}{-4t-6}`

Use the quotient rule to differentiate:
`f'(t)=frac{(-4t-6)(1/(2t^(1/2)))-(t^(1/2))(-4)}{(-4t-6)^2}`

`f'(t)=frac{(-2t-3)/(sqrtt)+4sqrtt}{(-4t-6)^2}`

`f'(t)=frac{(-2t-3+4t)/(sqrtt)}{(-4t-6)^2}`

`f'(t)=frac{2t-3}{(sqrtt)(-4t-6)^2}`