find derivative of (2/t^2)+(1/t)+6-12t+20t

Question

anonymous · Answer

$$f(t) = \frac{ 2 }{ t ^{2} }+\frac{1}{t} +6 - 12t +20t$$
first, you'll want to simplify your equation by combinging the like terms.
$$f(t) = \frac{ 2 }{ t ^{2} }+\frac{1}{t} +6 +8t$$
Then you can format it in a way that'll make it easy to use the chain rule.
$$f(t) = 2 { t ^{-2} }+t^{-1} +6 +8t$$
now you can find f'(t) by differentiating through.
Here's a general example of what you want to do f(t) = a*t^{b}
f'(t) = a*(b-1)t^{b-1}
Do this for everything in the equation.
If it helps you visualize, $$f(t) = 2 { t ^{-2} }+t^{-1} +6 +8t$$ is equivalent to 
$$f(t) = 2 { t ^{-2} }+t^{-1} +6t^{0} +8t$$

anonymous · Answer

thanks so much, unfortunatly i miss typed the problem because it's 20t^2 instead of just 20t...