If s is a function of t, find the differential coefficient of s in 2t^2-3t/√t+1

Answer 1

Differential Coefficient Calculation

Problem Statement:

Given a function s(t) = (2t^2 - 3t) / (√t + 1), find the differential coefficient of s with respect to t.

Solution:

We use the quotient rule for differentiation. Let u(t) = 2t^2 - 3t and v(t) = √t + 1.

1. Differentiate u(t) = 2t^2 - 3t:

 u'(t) = d/dt(2t^2) - d/dt(3t) = 4t - 3

2. Differentiate v(t) = √t + 1:

 v'(t) = d/dt(√t) + d/dt(1) = 1/(2√t)

Apply the quotient rule s'(t) = (u'v - uv') / v^2:

s'(t) = (4t^(3/2) - 3√t + 3t^2 - 3t/2) / (t^(3/2) + √t + 2t)

Therefore, the differential coefficient of s with respect to t is:

s'(t) = (4t^(3/2) - 3√t + 3t^2 - 3t/2) / (t^(3/2) + √t + 2t)