To find the derivative of s with respect to r, we use the chain rule:
ds/dr = ds/dt * dt/dr
First, let's find ds/dt:
ds/dt = d/dt (t^2 + 3t) = 2t + 3
Now, let's find dt/dr:
r = 4t^3 - 27
dr/dt = 12t^2
dt/dr = 1 / (dr/dt)
dt/dr = 1 / (12t^2)
Putting it all together:
ds/dr = (2t + 3) * (1 / (12t^2))
ds/dr = (1 / 6t^2) + (1 / 4t)
Therefore, the derivative of s with respect to r is ds/dr = (1 / 6t^2) + (1 / 4t).
Suppose r =
4t
3−27
3
and
s = t
2 + 3t, determine ds
dr
1 answer