Finding derivatives

Question

suppose f(t)=3/t^2. calculate the derivative of f if (f(t+h)-f(t))/h as h approaches 0

Answer 1

Answer 2

f(t) = 3/t^2

f'(t) = denominator times derivative of numberator (which is zero) minus numerator times derivative of denominator, all over denominator squared = the derivative of f(t)

= -3(2t)/t^4

=-6/t^3= derivative of f(t)

if you try to solve the problem with the quotient difference, and get a different answer, you made a mistake somewhere

f(t) = 3/t^2

f(t+h) = 3/(t+h)^2

f(t+h)-f(t) = 3/(t+h)^2 - 3/t^2

put them over a common denominator

t^2(t+h)^2

(3t^2 -3t^2 -6th + 3h^2)/t^2(t+h)^2

= (-6th +3h^2)/t^2(t+h)^2

divide by h

= (-6t +3h^2)/ t^2(t+h)^2

let h= 0

= -6t/t^2(t^2)

= -6/t^3