# Thread: Help Needed !! Exponential Differentiation

1. ## Help Needed !! Exponential Differentiation

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

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: $\frac d{d(x)} \frac uv = \frac {u'v - uv'}{v^2}$

here, $u = 0.001$ and $v = (0.001t + 1)^2$

Easy way:

write as $F(t) = 0.001(0.001t + 1)^{-2}$ and use the chain rule

chain rule: $\frac d{dx} f(g(x)) = f'(g(x)) \cdot g'(x)$

thus we get, $F'(t) = -2(0.001)(0.001t + 1)^{-3} \cdot 0.001 = -0.000002(0.001t + 1)^{-3} = - \frac {0.000002}{(0.001t + 1)^3}$

3. ## 2 more questions

Here is my questions :

how to solve it step by step

1. e^((integrate 0 to t) 0.4 t dt)

2. [-d(0.001t +1)^-1 / dt] *[ 1/(0.001t +1)^-1]

Can anybody help me? Thanks

Here is my questions :

how to solve it step by step

1. e^((integrate 0 to t) 0.4 t dt)
$e^{\int_0^t 0.4 t \ dt}=e^{0.4 \int_0^t x \ dx}=e^{0.4 \left[x^2/2\right]_0^t}$

$=e^{0.4*t^2/2}=e^{0.2 \ t^2}$

Or did you want to differentiate this ?

5. Originally Posted by Moo
$e^{\int_0^t 0.4 t \ dt}=e^{0.4 \int_0^t x \ dx}=e^{0.4 \left[x^2/2\right]_0^t}$

$=e^{0.4*t^2/2}=e^{0.2 \ t^2}$

Or did you want to differentiate this ?
i think that was the answer. Do you know how to solve my second question?