   Chapter 10.2, Problem 1E

Chapter
Section
Textbook Problem

# Find dy/dx.1. x = t 1 + t ,   y = 1 + t

To determine

To find:dydx for the parametric equations x=t1+t and y=1+t.

Explanation

Given:

The parametric equation for the variable x is as follows.

x=t1+t

The parametric equation for the variable y is as follows.

y=1+t

Calculation:

Differentiate the parametric equation x with respect to t.

x=t1+tdxdt=(1+t)(1)t(1)(1+t)2

Apply differentiation formula ddx(uv)=v(dudx)u(dvdx)v2 in the above equation.

dxdt=1+tt(1+t)2=1(1+t)2

Differentiate the parametric equation y with respect to t.

y=1+tdydt=12(1+t)1/2

Apply differentiation formula (ddx(u)=dx2u) in the above equation

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