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

1 Answer
Nov 22, 2016

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}