Hi,
Can anybody help me. How to differentiate this one step by step? Thanks a lot for your kindness.
F(t) = 0.001/(0.001t + 1)^2 dt
Hard way:
Use the quotient rule: $\displaystyle \frac d{d(x)} \frac uv = \frac {u'v - uv'}{v^2}$
here, $\displaystyle u = 0.001$ and $\displaystyle v = (0.001t + 1)^2$
Easy way:
write as $\displaystyle F(t) = 0.001(0.001t + 1)^{-2}$ and use the chain rule
chain rule: $\displaystyle \frac d{dx} f(g(x)) = f'(g(x)) \cdot g'(x)$
thus we get, $\displaystyle F'(t) = -2(0.001)(0.001t + 1)^{-3} \cdot 0.001 = -0.000002(0.001t + 1)^{-3} = - \frac {0.000002}{(0.001t + 1)^3} $