   Chapter 14.5, Problem 13E

Chapter
Section
Textbook Problem

Let p(t) = f(x,y), where f is differentiable, x = g(t), y = h(t), g(2) = 4, g′(2) = −3, h(2) = 5, h′(2) = 6, fx,(4,5) = 2, fy (4,5) = 8. Find p′(2).

To determine

To find: The value of p'(2) using Chain Rule where p(t)=f(x,y) , x=g(t)andy=h(t) , and if g(2)=4 , g'(2)=3 , h(2)=5 , h'(2)=6 , fx(4,5)=2 , fy(4,5)=8 .

Explanation

Chain Rule:

“Suppose that z=f(x,y) is a differentiable function of x and y , where x=g(t)andy=h(t) are both differentiable functions of t then, z is differentiable function of t and dzdt=zxdxdt+zydydt ”.

Given:

The value of p'(t) using chain rule is as follows,

dpdt=fxdxdt+fy&#

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