Derivative and integral question?

Question

1. Derivative df/dt of the function

f(t) = a1 * e^ (-b1*t) + a2 * e^(-b2*t) .

My answer is:

(a1*b1*e^(b2*t)*loge + a2*b2*e^(b1*t)*loge) /

(e ^ (b2+b1)*t)

2. Integral of the function

f(t) = a1 * e^ (-b1*t) + a2 * e^(-b2*t)

My answer is:

-(a1*b2*e^(b2*t)+b1*a2*e^(b1*t))/(b1*b...

Am i right? if not, could anyone help me with the right answer and walk me through the process? Thanks!!!

Answer 1

I'm sorry, but you're wrong

1) remeber, you are taking derivative in addition. you can do it by part and the derivative of e^(-bt) is -be^(-bt), so we have

df/dt = -a1b1 e^(-b1t) - a2b2 e^(-b2t)

2) all we need to deal with is the coefficient and we need a constant b underneath. so, lets try F(t)= (-a1/b1) e^(-b1)t - (a2/b2)e^(-b2t)

check, if we take the derivative of F(t), we have

dF/dt = f(t) =  (-a1/b1)(-b1) e^(-b1)t - (a2/b2)(-b2)e^(-b2t)

= a1e^(-b1t)+a2e^(-b2t)