Question

How do you use the Quotient Rule to differentiate the function `f (t) = (cos (7t)) / t^5`?

Answer 1

I found: `f'(t)=-(7tsin(7t)+5cos(7t))/t^6`

Explanation:

The Quotient Rule can be written as:
Given `f(t)=(h(t))/(g(t))` then: `color(red)(f'(t)=(h'(t)g(t)-h(t)g'(t))/[g(t)]^2)`

In your case you get:

`f'(t)=(-7sin(7t)*t^5-5t^4cos(7t))/(t^5)^2=`
`=(-t^4(7tsin(7t)+5cos(7t)))/t^10=`
`=-(7tsin(7t)+5cos(7t))/t^6`