Calculating the Derivative

Question

Calculate the derivative by expanding or simplifying the function.

s(t)=(1-2(7t))/(7t)^(1/2)

ds/dt=?

What is the derivative?

Answer 1

s(t)=(1-2(7t))/(7t)^(1/2) is equivalent to s(t)=(1-14t) /√7t.

If f(t)=(1-14t) and g(t)=√7t, then we have s(t)=f(t)/g(t). As such, derivative s'(t)=(f'(t)g(t)-g'(t)f(t))/g(t)^2.

f'(t)=14 and g'(t)= 7(t^(-3/2))/2= 7/2t^(3/2). Subsequently, we may plug these into s'(t) which we obtain:

s'(t)=-(14t+1)/(2.√7.t^(3/2)).