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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}#

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