Differentiate the given function?
y= 6/t + 3/t^2 -5/sqrt(t)
dy/dt=?
Add the derivatives of each term. Apply the rule that the drivative of a*t^n is n*a*t^(n-1), is a is a constant.
5/sqrt(t) can be written 5*t^(-1/2), so for that one, a = 5 and n = -1/2
This was not a physics question. It is a beginning calculus question
To differentiate the given function y = 6/t + 3/t^2 - 5/sqrt(t) with respect to t, you can follow these steps:
Step 1: Rewrite the function using exponent rules and simplify where possible. Start by writing each term with a common denominator, which in this case would be t^2 * sqrt(t):
y = (6 * sqrt(t) + 3 - 5 * t) / (t^2 * sqrt(t))
Step 2: Expand the terms in the numerator:
y = (6 * sqrt(t) + 3 - 5t) / (t^2 * sqrt(t))
Step 3: Apply the power rule for differentiation. For each term, multiply the coefficient by the power of t and subtract 1 from the power:
(dy/dt) = [6 * (1/2) * t^(-1/2) + 0 - 5] / (t^2 * sqrt(t))
= [3/t^(1/2) - 5] / (t^2 * sqrt(t))
Step 4: Simplify and rearrange the terms:
(dy/dt) = (3 - 5 * t^(1/2)) / (t^(3/2))
The final answer for dy/dt is (3 - 5 * t^(1/2)) / (t^(3/2)).