Question

differentiate:
y(t)=(1)/(t+4e^t)

Answer 1

so i know well be using the product rule..but i just dont know what to do with it after i took the derivative

Answer 2

it's chain rule :
y= (t + 4e^t)^-1
dy/dt = [-(t + 4e^t)^-2] x derivative of (t + 4e^t)
dy/dt = [-(t + 4e^t)^-2] x (1 + 4e^t)

Answer 3

its a fraction 1 over t + 4e^t

Answer 4

\[[-(t + 4e^t)^-2] \times d(t + 4e^t)/dt\]
\[dy/dt = [-(t + 4e^t)^-2] \times (1 + 4e^t)\]

Answer 5

aha .. so you differentiate the outer as it is u^-1 ,, then multiply it by the derivative of the inner (t + 4e^t)
this is the chain rule
yes I make 1 over t + 4e^t = (t + 4e^t)^-1

Answer 6

did you understand ??

Answer 7

\[d/dx{\frac{1}{f(x)}=\frac{-f'(x)}{f^2(x)}}\] so you answer here is
\[\frac{-(4e^x+1)}{(x+4e^x)^2}\]