   Chapter 10, Problem 26RE

Chapter
Section
Textbook Problem

# Find dy/dx and d2y/dx2.26. x = 1 + t2, y = t − t3

To determine

To find: The expression of dydx and d2ydx2 for x=1+t2 and y=tt3 .

Explanation

Given:

The parametric equation for the variable x is as follows.

x=1+t2 (1)

The parametric equation for the variable y is as follows.

y=tt3 (2)

Calculation:

Differentiating (1) with respect to t we get,

dxdt=2t (3)

Differentiating (2) with respect to t we get,

dydt=13t2 (4)

Dividing equation (5) by (3) we get,

dydx=13t22t

dydx=12t232 (5)

Differentiating (5) with respect to t we get,

d2ydx2=ddt(dydx)dxdt (6)

Substitute equation (3) and (5) in (6) we get,

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